Various disturbances propagation analysis of district heating system based on the standardized thermal resistance method

Various heating disturbances and faults in the heating network are necessary to be controlled and handled by some intelligent heating strategies with the increasing complexity of the heating network. This paper constructed the dynamic modeling of the heating system using standard thermal resistance and obtained a dynamic heat current model of the heating system. On this basis, we analyzed the heat transfer performance of the heating system. Five disturbances are selected, including the behavior of users, indoor heat source, heat exchanger heat transfer performance deterioration, pipe blockage, and pipe leakage. The effects of different disturbances on the overall system and user side water supply temperature were obtained by establishing a dynamic model for segmented heating pipelines. Feasible control methods for the heating network and load side are sorted out, mainly changing the water supply's temperature and the water supply's flow rate to reduce the water supply's fluctuation. Five specific control strategies are proposed for five types of disturbances. Comparing the case without control and the case with control, the results show that the fluctuation of water supply temperature is significantly reduced, and the control strategies can reduce the impact of disturbances on the heat network system and customers and improve the comfort of customers in the presence of disturbances. under the disturbance of pipeline leakage, the method proposed in this article reduces the temperature fluctuation amplitude by 75% and the fluctuation duration by 60%.


| INTRODUCTION
With the rapid development of urbanization in China, more and more energy and resources are required for the operation of cities. Especially in the northern winter, the stable and efficient operation of the heating system is the basic condition to ensure the normal life of the residents of the north.The proportion of annual heating energy consumption to total energy consumption in China is increasing yearly.The energy utilization efficiency of the heating system is low.Developing renewable energy is very important as it can reduce pollution to the environment caused by heating. 1,2In addition to solar and biomass energy, geothermal energy can play an important role in decarbonizing the heating sector. 3 In addition to the high pollution caused by fuel, there are other problems to be solved in the heating system, such as the heat loss of the heat transmission pipe network and the heating on demand.Heating in the market has always been an important urban centralized heating system direction.The heat loss of urban centralized heating system is not only reflected in the boiler heat efficiency and pipe network heat loss, 4 but also closely related to the heating system scheduling.Improper heating will not only reduce the quality of heating but also reduce the heating experience of hot users.At the same time, uneven cooling and heating will affect the thermal efficiency of the entire heating system, causing serious heat loss.Therefore, achieving precise regulation of various hot users is crucial.For example, in some public places such as school classrooms and canteens, the heat supply at night can be appropriately reduced, achieving good energy-saving effects.In addition, fault identification and repair are also important. 5he concept and type of fault disturbance are different for the centralized heating system in the integrated energy system.Taking a typical centralized heating system as an example, it is a large-scale, large delay, and highly coupled multi-input multioutput system, with disturbances mainly concentrated on the energy side, grid side, and user side.With the increasing complexity of the heating network, there will be more and more heating disturbances and faults in the heating network.Heating disturbances and faults in the heating network will cause the indoor temperature of heat users not to meet the standard, and the energy consumption of the heating network will increase.Therefore, adopting more advanced and intelligent heating strategies is necessary to reduce heating disturbances and the impact of faults in the heating network.
At present, there are many energy-saving control measures for the heating system, mainly including improving the thermal efficiency of the boiler, optimizing the layout of the heat transmission pipe network, enhancing the thermal insulation performance of the heating pipe network, and carrying out reasonable flow distribution according to user needs. 6Under the guidance of carbon neutrality, clean heating has been endowed with new connotations, and the heating industry has begun to move toward a new era of intelligent heating.The smart heating system is a new generation of intelligent integrated energy management system, which is based on energy supply informatization and automation, with the deep integration of information system and the physical system as the technical path, using technologies such as the Internet of Things, spatial positioning, cloud computing, and information security to sense and connect various elements in the whole process of heating system, and using advanced technologies such as big data, artificial intelligence, modeling, and simulation to coordinate, analyze and optimize various resources in the system. 7At the same time, the intelligent heating system should also consider the issues of economy and security.The heating system constantly improves production efficiency and stability to cope with disturbances. 8As the complexity of the user load continues to increase, perturbations will become more frequent.It is necessary to identify disturbances and predict their propagation paths in the system in time and select the corresponding control strategies.Building a smart heating system combined with artificial intelligence will help improve the heating system's stability, better meet users' diversified needs and reduce energy consumption and pollutant emissions.
Researchers have done much work to simulate and optimize the heating system.Bobič et al. 9 proposed a theoretical model to describe the transient response of a plate-type countercurrent heat exchanger due to temperature disturbances at the inlet.Yang et al. 10 established a new user-side heat load model of the district heating system (BHLP-UN model), which improved the accuracy of the original hybrid model.Xie et al. 11 optimized the heating system's water supply temperature and radiator materials to enhance users' thermal comfort.Wang et al. 12 proposed a temperature transport and flow transport model to predict the heating system under disturbance and steady state.O'Dwyer et al. 13 presented a disturbance prediction strategy based on quantum having particle swarm optimization (Q-PSO) and principal component analysis (PCA).An advanced physical and statistical description of the disturbances can provide useful short-term disturbance forecasts. 14Compared with the systems, ultra-low temperature district heating (ULTDH) can reduce energy consumption. 15Disturbance in the heating system affects not only its system but also the power system through coupling elements, which affects the heating system. 16Dancker et al. 17 proposed a sensitivity factor method for the district heating system.The heating pipeline network can also be seen as an energy storage system that provides flexibility for cogeneration power plants, thereby reducing the investment cost of traditional power plant energy storage equipment. 18Kim et al. 19 proposed a method for obtaining an improved gray box architectural model from closed-loop data with an obvious unmeasurable disturbance that can be used in the heating system.Mobarakeh et al. 20 proposed an artificial intelligence system based on artificial neural networks to construct prediction models.Liu et al. 21introduced four correction factors to correct the temperature and flow of the working medium in the heating system.Wang et al. 22 established a multistage control model for a water heat coupled multiuser building heating system.Li et al. 23 established a multiobjective optimization model that includes carbon emissions.A shortest path model and a depth-first layout algorithm were also used to improve the quality and efficiency of heating system. 249][30] Wu et al. 31 optimized the control strategy for hot user buildings by considering outdoor temperature changes and uncertainties within the building.
In summary, the research on the mechanism of disturbances within a single component is relatively mature, and there are also studies on the coupling characteristics of two parts.However, there are shortcomings in the research on the types and propagation mechanisms of system-level disturbances, mainly focusing on identifying faults or regulating individual equipment.Control methods have not yet been explored from a system perspective, and the impact of source-side disturbances on heat users is limited to analyzing their heating load.There is a lack of detailed research on the advanced treatment of indoor temperature.Therefore, conducting an in-depth study on the propagation mechanism of disturbances in the central heating system and the system-level disturbance control methods is very important.
In this paper, the heat current method is used for dynamic modeling of heating systems, which reduces intermediate variables and improves computational efficiency while ensuring computational accuracy.Instead of targeting a particular equipment, the effects of perturbations are investigated from a system perspective.Indoor temperature is the main analysis index in this paper, the indoor temperature is maintained within the set range to ensure the thermal comfort of the users by regulating the temperature and flow rate of the supply water.This paper introduces a typical centralized heating system, constructs its dynamic heat current model based on the standard thermal resistance method, and analyzes the heat transfer path of the heating system.According to the classification of the causes of disturbance, it can be mainly divided into two categories: pipe failure and user behavior.Five different disturbance scenarios are listed under these two categories.The effects of these disturbances on the indoor comfort of the heat network and the users are investigated.Feasible control means are sorted out, mainly by adjusting the temperature and flow rate of the water supply.Five specific disturbance control methods are proposed.The case with the disturbance control strategy added is compared with the case without the disturbance control strategy, and the result is that the temperature fluctuation is reduced, and the thermal comfort of customers is improved.These strategies can also provide a reference for operating heating systems under disturbing conditions.

| PHYSICAL MODEL OF REGIONAL CENTRALIZED HEATING SYSTEM
Figure 1 shows the heating process of a typical regional central heating system.The regional total heat exchange station provides water from the primary heat network and transmits high-temperature hot water to the userside heat exchange station through pipes.The heat exchange station heats the return water of the user side secondary network through the heat exchanger, and the heated return water delivers heat to each heat user through the pipe of the user side secondary network.The return water continues to the user-side heat exchange station to complete the heating process.The heating system includes a heat exchange station, secondary network and secondary network pipeline, room radiator, building users, and so on.Establishing the physical model of the central heating system helps us consider all | 4613 links and dynamic processes in the system to propose optimal control strategies.

| DYNAMIC MODEL BASED ON STANDARD THERMAL RESISTANCE METHOD
The dynamic processes that need to be considered in the centralized heating system include the heat exchanger wall of the heat exchange station, the wall of the supply and return pipes, the wall of the indoor radiator, the indoor air, the heat storage and release capacity of the concrete wall of the enclosure, and the delay of the supply and return pipes.This paper will introduce the standard thermal resistance method for the above multiple processes to construct the system's overall dynamic heat current model.

| Model of heat exchanger
The heat exchanger is an important component of the heating system.Dynamic heat exchanger modeling is indispensable to analyze the heating system's dynamic process.For modeling the heat exchanger, the following assumptions are made in this paper: the heat exchange between cold and hot fluids and the environment is ignored, and only the heat exchange between cold and hot fluids is considered.The physical properties of the fluid remain the same.There is no heat transfer along the axial direction of the heat exchange surface; the heat transfer coefficient of the heat exchanger surface does not change.The flow rate and heat capacity of the fluid remain constant.There is no internal heat source for the fluid and the heat exchanger.
Figure 2 is a schematic diagram of the physical model of the heat exchanger.The temperature of the hot fluid entering the heat exchanger is T h , the flow rate is G h , the temperature of the cold fluid entering the heat exchanger is T c , the flow rate is G c , the temperature of the heat exchanger wall is T b , and the heat exchanger length is L. Both the hot and cold fluids flow horizontally.
In the countercurrent heat exchanger, the flow direction of the hot and cold fluids is opposite.The transient energy conservation equation for hot and cold fluids can be expressed as Under the assumptions of this paper, the dynamic expression of the temperature of the tube wall in the heat exchange process with time can be derived based on the heat current method 32 where M is the mass of the heat exchanger surface, and c p is the heat exchanger wall's heat capacity.R h is the thermal resistance between the thermal fluid and the heat exchanger wall, and R c is the thermal resistance between the thermal fluid and the heat exchanger wall.The left side of the equation represents the change in temperature, the first term on the right represents the heat transfer from the hot fluid to the wall, and the second term represents the heat transfer from the wall to the cold fluid.The expressions of R h and R c are NTU h and NTU c are the numbers of heat transfer units at the hot end and the cold ends, 33 indicating the ratio of the effective thermal conductivity of the heat exchanger to the heat capacity flow rate of the hot and cold fluids.They can be written as follows: φ is a correction factor used to represent the impact of heat exchanger processes on heat transfer performance.k is the heat transfer coefficient.A is the heat exchange area, G h and G c are the thermal capacity flows of hot and cold fluids, respectively, representing the product of mass flow rate and specific heat, the formula can be written G m c = .
Heat exchange occurs between the cold and hot fluid and the heat exchanger wall.Based on the energy conservation law, the outlet temperature can be derived.
When the heat transfer process tends to a steady state, the heat exchanger wall temperature tends to stabilize and can be expressed as The standard thermal resistance is introduced, and a dynamic heat current model for the heat exchanger is established through thermoelectric analogy. 34T h denotes the inlet temperature of the hot fluid of the heat exchanger, T c is the inlet temperature of the cold fluid of the heat exchanger, T w is the surface temperature of the heat exchanger wall, R h and R c represent the thermal resistance between the hot and cold fluid and the wall respectively, and C w represents the heat capacity of the heat exchanger wall.The specific schematic is shown in Figure 3.

| Model of water supply and return pipe
Due to environmental and other factors, the pipes of the secondary transmission network in the heating system are usually buried underground.Heat fluids inside the pipes will exchange heat with the soil, resulting in heat loss.To reduce the heat loss in the heating pipes, there is a layer of insulation outside the heating pipes, and the thermal fluid passes through the pipe wall and the insulation layer to exchange heat with the soil.There is only one type of thermal fluid present in the heating pipe, the temperature of the pipe wall is T p , the length of the pipe is L d , the temperature of the thermal fluid at the inlet end is T d,in , and the velocity of the thermal fluid flowing in the pipe is v, the soil temperature in the environment is T s .The heating pipes are usually long, and there is a delay in the heating process, so the secondary pipe network is considered to have heat storage ability.In this paper, the pipeline modeling for the secondary network adopts a segmentation approach, dividing the pipeline into n heat transfer units, and the dynamic heat transfer process is calculated independently for each unit.Figure 4 shows the pipeline's overall and segmented units' models.
The expressions describing the heat transfer process of the fluid and pipe wall in the pipeline can be expressed as where R s,i is the total thermal resistance of the steel pipe and the two layers of external insulation, i in the subscript indicates the serial number of the heat transfer unit of the pipe, and its thermal fluid outlet temperature is the inlet temperature of the thermal fluid of the next unit.c p is the heat capacity of the pipe wall.
Figure 4 shows the physical model of the heating pipeline.In combination with the heat current method, the dynamic model of the segmented pipeline unit can be obtained, as shown in Figure 5.
The length of secondary network pipelines is usually very long, with a significant delay in temperature propagation.To express the impact of this delay on the heating network, this paper introduces the concept of inductance based on thermoelectric analogy and uses thermal inductance RL to represent the delay in the pipeline heat transfer process.For the heat transfer process of a unit, it is assumed that the time required for the hot fluid to flow from the unit inlet to the outlet is τ, the temperature drop caused by the heat exchange between the hot fluid and the environment is ΔT.The following expression can represent the outlet temperature of the hot fluid in this unit.
For the heat transfer unit, the time τ required for the working medium to flow as a function of length and flow rate can be expressed as

| Building model with indoor air and walls
For the building model in which the heat users live, due to a large number of rooms, and to improve the calculation's efficiency, this paper reduces the room in which each user lives to a rectangular body for the calculation.For each room, the main factors affecting the temperature of the water supply are considered, including the temperature of the outdoor environment, the area to be heated, the thickness of the envelope and the physical properties of its materials.The building model in this paper also considers the thermal storage capacity of the various parts of the walls, radiators, and air.
Figure 6 shows the room model.The length, width, and height of the room are 4, 3, and 3 m, respectively, with a U-value of 0.24 W/(m 2 •K), and there is no additional internal heat source.
When building the room model, the following assumptions were put forward: (1) ignoring the difference of solar radiation in each room; (2) the temperature distribution in all parts of the room is uniform and the same value; (3) ignoring the heat loss caused by air leakage, the radiator is the only heat source in the room, ignoring the heat transfer between rooms.Based on the above assumptions, the following expression can be obtained to describe a room's dynamic heat transfer process.
Q is the heat transfer rate between the hot fluid and the heat exchanger wall, and G l is the indoor fluid's heat capacity and flow rate.The wall temperature of the radiator, indoor air, and the heat capacity of the indoor wall are represented by C r , C a , and C w ."r" represents the heat exchanger wall, "a" means the indoor air, "b" represents the wall, and "e" represents the outdoor air.T l represents the inlet temperature of the radiator fluid, T r represents the wall temperature of the radiator, the indoor temperature is represented by T a , and the wall temperature and outdoor temperature are represented by T b and T e , respectively.Figure 7 shows the schematic diagram of the dynamic heat current model for a single room with the introduction of standard thermal resistance.

| Overall dynamic model of central heating system with user
Figure 8 shows a dynamic model of a central heating system using the heat flow method, which includes multiple heat exchange processes.RL and RL' represent the delay in the pipeline heat transfer process.Starting from the hot fluid inlet at the heat exchange station, heat flows from the hot fluid to the cold fluid at the heat exchange station, followed by heat exchange between the water supply and the surrounding environment on the way to the secondary network supply piping, and heat flows from the water supply to the environment.The heat exchange occurs in the radiator after the supply of water reaches the user side, and the heat flows from the water supply to the indoor air.The heat of the return water in the return pipeline also flows to the environment, ending at the cold fluid inlet of the heat exchanger station.The above is the heat transfer process in the heating system.With this model, the path of heat transfer can be seen clearly.

| DISTURBANCES ANALYSIS BASED ON DYNAMIC HEAT CURRENT MODEL
Due to the characteristics of multiuser participation, multidevice coupling, and asynchronous delay in heating networks, overall modeling and analysis of multiuser participation in heating networks is the basis for analyzing disturbance propagation.Based on the established the overall dynamic heat current model of the central heating system, this chapter studies and analyzes the propagation and evolution law of disturbances in the heating network and formulates different heating strategies for various disturbances.Disturbance of indoor heat sources can cause an increase in indoor temperature.User behavior disturbances can cause irregular fluctuations in indoor temperature.Pipeline leakage disturbances can cause a decrease in indoor temperature.The degradation and disturbance of heat exchanger performance will gradually reduce the indoor temperature.Pipeline blockage and disturbance can cause an increase in heating temperature.

| Without disturbance
When there is no disturbance, Figure 9 presents the changes of indoor and heating temperatures.Due to the continuous changes in outdoor temperature, the indoor temperature shows a wavy trend, with a maximum temperature of 18.81°C and a minimum temperature of 18.31°C.At this time, the energy consumption of the heating strategy is 37.80 W/m 2 .

| Indoor heat source disturbance
In daily life, various indoor activities can cause changes in indoor temperatures, such as cooking, using household appliances, gatherings, and so on, affecting indoor heat users' comfort.This section will use dynamic simulation methods to study the impact of heating disturbances and propose countermeasures.When the disturbances range from 1:13 to 17, there exists an internal heat source with a power of 500 W; Disturbance 2: There is an internal heat source with a power of 1000 W between 13 and 17.Internal heat sources can cause an increase in indoor temperature, affecting the user experience.If the indoor temperature rises too much, it affects the user experience and generates energy waste.When facing heating disturbances, it is necessary to adopt new heating strategies to improve user heating experience and save energy.
Figure 10 shows the impact of different perturbations under the same outdoor temperature and corresponding heating strategy.In this case, condition 1 indicates that no perturbation occurred in the heating system, condition 2 indicates that the heating system experienced a 500 W internal heat source perturbation, and condition 3 indicates that the heating system experienced a 1000 W internal heat source perturbation.In condition 2, the maximum indoor temperature is 20.54°C, which is an increase of 1.73°C compared to the maximum temperature of 18.81°C without disturbance.After condition 3, the maximum indoor temperature was 22.28°C, which increased by 3.47°C compared to the maximum temperature without disturbance and 1.74°C compared to condition 2. Due to the disturbance of internal heat sources indoors, the excess heat generated inside is absorbed by the indoor walls and radiator walls, increasing the heat capacity of the walls and radiator walls, resulting in an increase in indoor thermal inertia and a decrease in the rate of indoor air decline.Therefore, after the disturbance, the indoor temperature of condition 3 is always higher than that of condition 2.
Under the disturbance response heating network strategy, the indoor temperature changes are shown in Figures 11 and 12.The primary network heat exchanger reduces the heating temperature after the disturbance occurs, and exhibits a step like change over time.There is a brief increase before the disturbance ends.The average heating energy consumption of the heating strategy in condition 2 is 35.97W/m 2 .The average heating energy consumption of the heating strategy in condition 3 is 35.05W/m 2 , which is compared to the energy consumption of 37.80 W/m 2 in condition 1, The energy-saving ratios are 4.84% and 7.28%, respectively, indicating that the new heating strategy has saved energy.At the same time, under the new heating strategy, indoor temperature fluctuations are reduced compared to not taking measures, eliminating the phenomenon of indoor overheating caused by disturbances and lower user comfort.F I G U R E 10 Indoor temperature under disturbance 1 and disturbance 2 when using the original heating strategy.
F I G U R E 11 Heating strategy and indoor temperature adopted in response to disturbance 1.
Comparing the two heating strategies calculated, after the disturbance occurred, the heat released during the duration of disturbance 2 was twice that of disturbance 1, but the energy savings were not less than twice.When the heat released during the duration of the disturbance is higher, the average temperature inside the room is higher, which increases the heat emitted from inside the room to the outside.Therefore, not all the heat released by the internal heat source can be used to save energy consumption.

| User behavior disturbance
Thermal users are the service objects of the central heating system.Ensuring the normal use of heat by users and maintaining the comfort level of thermal users are important optimization objectives of central heating system.However, thermal users have the characteristics of wide distribution and strong uncertainty of behavior.The disturbance of the thermal network will affect the users' indoor temperature, and the users' behavior will also have an impact on the thermal network.In this study, a heating strategy of district heating system based on user behavior prediction is proposed, which solves the problem of user behavior uncertainty and heating demand response, and ensures users' comfort level.This paper assumes that the heat user opens the window for ventilation at 13:00 and closes the window at 17:00. Figure 12 shows the temperature change diagram of the primary network under various working conditions.Working condition 1 shows no disturbance in the heating system, working condition 2 indicates a disturbance in the heating system but no response strategy is taken, and working condition 3 shows that the heating system predicts the disturbance and adopts the corresponding heating strategy.The temperature curve of the primary network heating in condition 1 is stable; The heating curve of the primary network of the system in condition 2 is the same as when there is no disturbance; Due to the presence of certain heating delays in the pipeline network, the control strategy adopted in this paper is based on user daily behavior prediction, that is, changing the heating strategy before user behavior occurs to ensure that the indoor temperature is within the appropriate temperature range.The system's response strategy is shown in the curve of condition 3, where the heating temperature changes between 50°C and 95°C.
According to the hourly heating temperature of the primary network, as shown in Figure 13, indoor temperature changes under three heating strategies are obtained, as shown in Figure 14.In working condition 3, the indoor temperature has been kept in the temperature range of 18-19, which has been improved compared with the lowest temperature of 16.97°C in working condition 2, thus reducing the influence of disturbance on indoor temperature and ensuring the comfort of thermal users.As seen from Figure 14, the temperature of working condition 2 dropped rapidly after 13 h, and reached the lowest value of 16.98°C 45 min later.The indoor temperature rose again until the window was closed at 17 h and the indoor temperature of working condition 2 was lower than that of working condition 1 during 17-24 h.When working condition 3 is at 13, the indoor temperature is kept between 18°C and 19°C because the heating temperature is changed in advance.In condition 3, although the temperature of primary network water F I G U R E 12 Heating strategy and indoor temperature adopted in response to disturbance 2.
F I G U R E 13 Heating temperature curve.
supply is increased and the heating energy consumption is increased, the active ventilation needs of thermal users are satisfied, and the indoor temperature is kept stable.

| Pipeline leakage disturbance
Heating pipelines are an indispensable component of urban pipeline systems, but as the age of heating pipelines increases year by year, various phenomena of open or hidden leaks may occur in heating pipelines.Therefore, it is particularly important to explore the pipeline leakage disturbance.
Assuming that the heating pipeline leakage occurs at 13:00, the pipeline's flow is halved, the company completes the maintenance at 17:00, and the normal heating flow is restored.As shown in Figure 15, working condition 1 is that no disturbance occurs in the heating system; working condition 2 is that the heating system leaks but no coping strategies are taken; working condition 3 is that the heating system leaks and corresponding heating strategies are taken.In working condition 1, the heating temperature curve of the system's primary network is stable and always at 74.40°C.In condition 2, no measures are taken for the heating system, and the heating curve of the primary network is the same as that without disturbance.For the leakage condition, the heating system predicts the disturbance.It changes the heating strategy of the primary network so that the indoor temperature returns to the appropriate temperature range as soon as possible.After the indoor temperature reaches the heating demand, the design condition continues to be used for heating.
According to the hourly heating temperature of the primary network shown in Figure 15, the indoor temperature changes under three heating strategies are obtained as shown in Figure 16.The indoor temperature in condition 1 has been maintained within the temperature range of 18-19; Under condition 2, the indoor temperature gradually decreases after 13:00 and reaches a minimum temperature of 17.73°C at 17:00.After the disturbance ends, the heating flow returns to normal and the indoor temperature rises.However, in the subsequent time, the indoor temperature is lower than condition 1; Under condition 3, due to the increase in the heating temperature of the primary network, the impact of water leakage on indoor temperature is reduced, and the fluctuation of indoor temperature is reduced.However, increasing the water supply temperature of the primary network after a water leakage fault increases the system heat consumption.The actual situation can be balanced between energy consumption and user comfort.

| Heat exchanger performance degradation disturbance
Heat exchanger fouling is an extremely common phenomenon, and its hazards mainly include deteriorating heat transfer performance, increasing energy consumption and increasing initial investment on.The harm is enormous.In summary, the impact of dirt on the heat transfer performance of heat exchangers cannot be ignored.This paper conducts the following research on the effect of fouling on the heat transfer performance of the heat exchanger surface: showing an indoor temperature analysis with a period of 100 days, assuming that the outdoor temperature is constant at −10°C, and assuming that the heat transfer coefficient of the structure decreases by 3 W/(m 2 •K) per day.Without changing the primary network heating temperature of 74.40°C, the average indoor temperature within 100 days decreases by about 0.55°C.Therefore, because of the heat exchanger structure caused by the performance decline, to meet the heating requirements, the measures taken to increase the network heating temperature once a day, the calculation of the daily increase is 0.025°C.Figure 17 shows the indoor average temperature change after a daily increase of heating temperature under structural conditions and control conditions for 100 days.

| Pipeline blockage disturbance
One of the most common faults in heating systems caused by foreign object blockage is that the blockage causes the heating system to not be hot, resulting in the user's room temperature not reaching the specified temperature and affecting user comfort.Assuming that the secondary network water supply pipeline is completely blocked at 13:00 and heating is restored at 17:00.As shown in Figure 18, condition 1 is that no disturbance occurs to the heating system, so the primary network heating is always at 74.40°C; condition 2 is that the heating system is blocked but no countermeasures are taken, and the heating curve of the system's primary network is the same as that without disturbance; Working condition 3 is when the heating system is blocked and the corresponding heating strategy is adopted.The heating system predicts the occurrence of disturbance.It changes the heating strategy of the primary network to make the indoor temperature return to the appropriate temperature range as soon as possible.After the indoor temperature reaches the heating demand, the design working condition will continue to be used for heating.
Figure 19 is a diagram of indoor temperature changes for the leakage condition.Both conditions 2 and 3 reached a minimum temperature of 8.46°C.However, due to the higher water supply temperature in condition 3 than in condition 2, the indoor temperature reached 18°C at 17:45 in condition 3, which is earlier than the user's daily return time from work and about 75 min earlier than in condition 2, effectively improving the comfort of hot users.In this paper, the typical central heating system is taken as the object, combined with the heat current model, considering the disturbance factors such as failure, environment and human, and so on, to explore the influence of different disturbance causes on the heat network and the indoor comfort level of users, sort out the feasible control means of the heat network, and provide coping strategies under different disturbances.The main research contents are summarized as follows.Five typical heating system disturbances in a single thermal user are analyzed: internal heat source disturbance, user behavior disturbance, pipeline leakage disturbance, heat exchanger performance decline disturbance, and pipeline blockage disturbance.Based on the influence of disturbance on the heating system, combined with the automatic control theory, indoor comfort level is the first goal and the corresponding control method is studied.Different intelligent heating control methods and disturbance control strategies are calculated to reduce the influence of disturbance on the system.Compared with traditional systems, the method proposed in this article reduces the amplitude of temperature fluctuations under different disturbances and shortens the duration of fluctuations, effectively improving the stability of the heating system and enhancing the thermal comfort of users.For example, under the disturbance of pipeline leakage, the method proposed in this article reduces the temperature fluctuation amplitude by 75% and the fluctuation duration by 60%.Under the disturbance of heat exchanger performance degradation, the temperature loss decreases by 0.55°C.The study and proposal of quantitative metamorphic heat supply regulation strategies adapted to different heat demands can provide a basis for heat supply companies to reasonably formulate and adjust heat supply schemes to ensure the comfort level of thermal users in the face of diversified heat demand.Currently, this paper focuses on the heating pipe network side.In the future, the heat current method will be used to consider the distribution of urban distribution networks and heat exchange stations, and comprehensive energy system modeling will be introduced to realize the cooperation of the source network and contribute to the realization of intelligent heating.

F I G U R E 3
Dynamic heat current model of a single heat exchanger.F I G U R E 4 Overall physical and segmented model of the pipeline.CHEN ET AL.

F I G U R E 5
Dynamic heat current model of a unit in the pipeline.F I G U R E 6 Schematic diagram of the building envelope.

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I G U R E 7 Dynamic heat current model of the building envelope.F I G U R E 8 Overall dynamic heat current model of central heating system with users.

F I G U R E 9
Heating temperature and indoor temperature changes.

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I G U R E 14 Indoor average temperature curve.F I G U R E 15 Heating temperature curve.F I G U R E 16 Indoor temperature curve.

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I G U R E 17 Average indoor temperature curve.F I G U R E 18 Temperature variation diagram of primary network water supply for plugging condition.
NOMENCLATURE A heat transfer area, m 2 c p specific heat capacity, W•kg −1 •K −1 G heat capacity flow, W/K k heat transfer coefficient, W•m −2