Research on multi‐time scale modeling and interaction of electro‐thermal coupling integrated energy system

With the enhancement of the coupling degree and interaction of the electro‐thermal integrated energy system, the fault propagation characteristics under multi‐time scale characteristics become more complex, which may trigger cascading failures and affect the safe operation of the system. Therefore, this article proposes to construct a multi‐time scale comprehensive model based on the steady‐state model and quasi‐dynamic model of electro‐thermal coupling integrated energy system, and uses the strategy of global iteration combined with local simultaneous solution to calculate the energy flow distribution of electro‐thermal coupling system under multi‐time scale. Combined with the characteristics of multi‐time scale energy flow distribution, the interaction mechanism and the fault propagation process of electro‐thermal coupling are analyzed. The simple electro‐thermal coupling integrated energy system and Barry Island electro‐thermal coupling integrated energy system are used as examples to analyze the electro‐thermal coupling characteristics and interaction of the system. The calculation results show that the disturbance of both electrical and heat loads will have a certain impact on the power system and heating system. Due to the thermal inertia of the heating system, there is a large time delay of fault propagation in the heating system. In the process of operation and scheduling of the electro‐thermal coupling integrated energy system, the slow dynamic characteristics of the heating system and the positive effect of thermal inertia on resisting the uncertainty factors in the system should be fully considered.


Abstract
With the enhancement of the coupling degree and interaction of the electro-thermal integrated energy system, the fault propagation characteristics under multi-time scale characteristics become more complex, which may trigger cascading failures and affect the safe operation of the system. Therefore, this article proposes to construct a multi-time scale comprehensive model based on the steady-state model and quasi-dynamic model of electro-thermal coupling integrated energy system, and uses the strategy of global iteration combined with local simultaneous solution to calculate the energy flow distribution of electro-thermal coupling system under multi-time scale. Combined with the characteristics of multi-time scale energy flow distribution, the interaction mechanism and the fault propagation process of electro-thermal coupling are analyzed. The simple electro-thermal coupling integrated energy system and Barry Island electro-thermal coupling integrated energy system are used as examples to analyze the electro-thermal coupling characteristics and interaction of the system. The calculation results show that the disturbance of both electrical and heat loads will have a certain impact on the power system and heating system. Due to the thermal inertia of the heating system, there is a large time delay of fault propagation in the heating system. In the process of operation and scheduling of the electro-thermal coupling integrated energy system, the slow dynamic characteristics of the heating system and the positive effect of thermal inertia on resisting the uncertainty factors in the system should be fully considered.
in the future. Among them, the electro-thermal coupling IES will be rapidly developed and applied in the middle and high latitudes of the world. However, with the deepening of electro-thermal coupling, its multi-time scale characteristics cannot be ignored, which is not only the core of the operation and scheduling of electro-thermal coupling IES, but also the key of multi-time scale modeling.
Scholars at home and abroad have done a lot of research work on IES modeling. 3 The concept and model of energy hub (EH) was first proposed by Swiss Federal Institute of Technology in 2005, where EH described the input and output relationships of a multi-energy flow system through a coupling matrix. The concept of EH is clear and the mathematical form is simple, but it is difficult to describe the nonlinear and dynamic behavior of complex systems and the topological relationship of complex networks. 4,5 Reference 6 optimized the energy hub (EH) model and established the coupling model of heating network and cooling network. The coupling model can describe the flow of energy flow and network flow at different nodes, which can not only represent the topological structure of the network, but also reflect the attributes and limit constraints of energy flow. However, it does not consider the slow dynamic process of the heating system. References 7,8 deduced the thermal circuit model and hydraulic circuit model in the heating system by using the form of bus similar to power system, and simplified the model to algebraic equation by Fourier transform and two-port equivalence, thus forming the hydraulic network model and thermal network model of the heating system, which can describe the branch characteristics and topological constraints of the heating network. In the above modeling process, the heating system model was simplified. Through the unified modeling method, the complexity of the multi-energy flow coupled system model can be reduced, but these models are suitable for large-scale energy transmission networks.
In the electro-thermal coupling energy system, electrical energy is transferred at the speed of light in the power grid, while heat energy is transferred at the speed of fluid in the heat network, with a general speed of 0.35-0.5 m/s, which is greatly different from the electrical energy transmission speed. For this reason, when the steady-state model is used to analyze the energy flow distribution of the electric-thermal coupling system, the large inertia and slow dynamic process of the heat network are not taken into account, which makes it difficult to accurately describe the regulation process in operation. 9 Therefore, it is necessary to introduce a dynamic model of heat network, obtain the transmission characteristics of multiple energy flows at multiple time scales by solving the partial differential-differential-algebraic equations of the electro-thermal coupling system, and further analyze the transmission process under system fault disturbance. Regarding the dynamic model of the heat network, the Reference 10 proposed to use the node method to describe the temperature transfer process and established a thermal quasi-dynamic model considering the delay, but the thermal model was linear. Reference 11 simplified the node method and expressed the outlet temperature with the inlet temperature at the time before the transmission delay to establish a thermodynamic quasi dynamic model. Reference 12 pointed out that the heat network model established by node method simplified the pipeline into nodes and heat exchange stations, which cannot fully reflect the heat storage and dynamic characteristics of the heat network.
In addition to using the node method to describe the dynamic characteristics of temperature, the Reference 13 proposed to solve the slow dynamic process of the heating system by simulating the heat loss and transmission delay through modeling under the unified framework of the Laplace domain in view of the fact that the dynamic characteristics of the heating system are still not fully described. References 13, 14 ignored the internal heat transfer of the fluid, obtained the relationship between the relative temperature of the pipeline and space and time through Laplace transform and inverse transform to establish a dynamic model of heat network reflecting the characteristics of heat transfer. The thermal quasi-dynamic model with delay coincides with the actual thermal system scheduling strategy, and the transmission dynamic characteristics and heat storage characteristics of the heat network can be fully considered. Reference 15 proposed a refined modeling method that takes into account the heat network and heat load. The dynamic process of heat transmission is described in detail by establishing a heat network transmission model and a building energy storage characteristic model. However, the established model still used an algebraic equation with a certain time delay, which cannot describe the change process of each state variable under disturbance. Reference 16 described the slow dynamic process of the heating system by using thermal inertia, which consists of two parts: heat transmission delay and building heat storage. The thermal inertia characteristics are described by the heat supply pipe network and building heat transmission delay, which is also modeled using algebraic equations.
The model of electro-thermal coupling IES is the premise of multi-energy flow calculation. At present, there are two main methods for calculating multi-energy flow distribution: unified power flow method and decomposition iteration method. The idea of unified power flow method is intuitive, but because of the large gap between power and heating systems in time scale, the unified modeling will cause the singularity of Jacobian matrix, which is difficult to converge. At the same time, the unified power flow method cannot consider the slow dynamic process of the heating system. The decomposition iteration method can improve the calculation speed by connecting the power and heating systems with coupling elements, but there are also some problems. For example, the Reference 17 pointed out that the interaction between systems may also occur non convergence in the iteration process, which needs further in-depth study. Reference 18 only considered the convergence properties of heat network power flow and power grid power flow itself in the calculation process, and did not analyze the overall convergence properties. In Reference 19, a linear model of regional heating network was derived based on the assumption of equivalent infinitesimal replacement theorem and approximate equality of supply temperatures at load nodes, and the feasibility of the model was verified by optimal scheduling calculations. Reference 20 established a regional heating network model considering the thermal inertia of heating pipelines and buildings. The research results show that the thermal inertia causes the time shift of heat load, effectively improves the operational flexibility of the electro-thermal coupling system, and actively responds to the uncertainty of the system. References 21, 22 proposed a solution method of electro-thermal coupled energy system considering dynamic model, but it is still far from practical application. The main reason is that the model is relatively simple and does not take into account the characteristic differences between different energy flow systems. In a word, the multi-time scale modeling and solution of electro-thermal coupling IES considering the slow dynamic process of heating network is still in its infancy.
In this article, the steady-state model and quasi-dynamic model of electro-thermal coupling IES under multiple time scales are proposed, and the global iterative-local simultaneous solution method is adopted to analyze the multi-energy flow transmission characteristics and interaction of electro-thermal coupling IES under multiple time scales. The interaction and fault propagation characteristics of the electric-thermal coupling system under multiple time scale are further verified by examples, which provides a theoretical basis for the planning and scheduling of the electric-thermal coupling IES. The main innovation points of this article are: 1. The steady-state model, quasi-dynamic model, and multi-time scale comprehensive model of electro-thermal coupling integrated energy system are constructed. 2. According to the characteristics of multiple time scale, the method of global iterative combined with local simultaneous solution is proposed to calculate the energy flow distribution of electro-thermal coupling integrated energy system, which solves the problem that it is difficult to converge in the unified energy flow calculation of integrated energy system.
The remainder of this article is organized as follows. Section 2 constructs the structure of electro-thermal coupling integrated energy system. According to the models of power system, heating system, and coupled element, taking into account the thermal dynamic process of heating network thermodynamic system and heat load, a multi-time scale integrated model of minutes and above is established, and a global iterative combined with local simultaneous strategy is proposed to solve the electro-thermal coupling energy flow distribution. In Section 3, the coupling relationship between power system and heating system is analyzed, and the interaction mechanism and fault propagation mechanism of electro-thermal coupling system are studied. In Section 4, a typical electro-thermal coupling system is used as an example to verify the feasibility of multi-time scale model and the interaction mechanism of electro-thermal coupling system. Section 5 concludes this article.

System structure
The structure of electro-thermal coupling IES mainly includes three parts: power system, coupling system, and heating system, as shown in Figure 1.
As can be seen from Figure 1, the coupling element in the coupling system is the key component of the electro-thermal coupling IES, which provides the basis for the electro-thermal synergy. The construction of a new power system with renewable energy as the main body and the promotion of green and low-carbon energy development is the development direction of China's power system. Therefore, give full play to the power market to regulate energy supply and promote renewable energy consumption, electric boilers (EB) based on time-sharing tariffs as well as heat pumps (HP) will play an active role in the heating system. The coupling degree of the power and heating system is more in-depth, and the significance of establishing a dynamic model of the heating system is more important. Considering that the response speed of the power system is faster than that of the heating system, therefore, only the thermal system in the heating system is dynamically modeled when the dynamic modeling of the electro-thermal coupled multi energy flow system is performed. The power system uses the node power balance equation model, specifically: where P i and Q i represent the active and reactive power of the power system, respectively; U i and U j represent the voltage amplitudes of nodes i and j, respectively; G ij and B ij represent the conductivity and susceptance, respectively; and ij represents the power angle between nodes i and j.

Heating system model
The heating system mainly consists of a heat source, a heat supply network, and a heat load. The heat source provides heat to the heat load through the heat supply network, and its mathematical model is: where c p represents the specific heat capacity of the heat source medium, m represents the flow rate of the heat source, T s represents the output temperature of the heat source, and T r represents the return temperature of the heat source. The heat supply network realizes the transmission and distribution of heat through the flow of medium. Therefore, there are two processes in the heat supply network, namely, hydraulic and thermal. The hydraulic process describes the medium flow, the thermal process describes the heat flow, and the dynamic process of hydraulic is much faster than the thermal. Therefore, the hydraulic and thermal processes are often analyzed separately, in which the hydraulic process is analyzed by the steady-state model and the thermal process is analyzed by the steady-state or dynamic model.
The hydraulic steady-state model describes the relationship between flow and nodes, as well as the relationship between pressure and ring network, and its mathematical model are as follows: where A h represents the node-branch incidence matrix of the heat supply network, m represents the column vector of the branch flow of the heat supply network, m n represents the column vector of the node flow of the heat supply network, B h represents the loop-branch incidence matrix of the heat supply network, and Δp represents the column vector of branch voltage drop. Among them, the calculation formula of Δp is: where R h represents the resistance coefficient of the heat supply network pipeline, represents the medium density, g represents the gravitational acceleration, Δh represents the height difference of the branch sea wave, and Δp cp represents the pressure source present in the branch, such as the circulation pump. After the medium flowing into the node is mixed at different temperatures in the heat supply network, it is generally considered that the mixing is sufficient and the temperature of the medium flowing out of the node is the same. And the node meets the law of conservation of energy, that is, the total energy flowing into the node is equal to the total energy flowing out of the node, that is: where T n,in and T n,out represent the temperatures of the inflow and outflow nodes, respectively; m n,in and m n,out represent the flow rates of the inflow and outflow nodes, respectively; and c p,n,in and c p,n,out represent the specific heat capacities of the inflow and outflow node medium, respectively. In the heat transfer process, the influence of valves, circulation pumps, and other equipment on the temperature can be ignored relative to the heat transferred by the medium. The thermal dynamic model of the heat supply network mainly describes the process of temperature propagation along the pipeline, which is described by partial differential equations proposed in this article, specifically: where T p and T p,a represent the pipe temperature and pipe ambient temperature, respectively; k p represents the thermal conductivity of the medium, A p represents the cross-sectional area of the pipe, and R p represents the thermal resistance per unit length of the pipe.
Considering that k p A p (6) is negligible compared to the other terms, so that Equation (6) can be simplified as: When the flow rate of the pipe is constant for a certain period of time, then the temperature at the outlet of the pipe is obtained as: where T p,out (t) and T p,in (t) represent the pipe output and input temperatures, respectively; t d represents the transmission delay of the pipe; and p represents the thermal conductivity of the transmission medium. The thermal steady-state model of the heat supply network describes the relationship between the temperatures of each node in the heat supply network under the condition of steady-state operation. At this time, T p,in and m are set to be constant on the basis of the dynamic model, the steady-state model can be obtained as follows: where L represents the length of the pipe.
As an important equipment of the heat network system, the heat exchanger transfers heat from the primary side with high temperature to the secondary side with low temperature, and is decoupled in the hydraulic model. Among them, the heat transmitted by the primary side, the secondary side, and the heat exchanger are as follows: where T h1,in and T h1,out represent the inlet and outlet temperatures of the primary side, respectively; T h2,in and T h2,out represent the inlet and outlet temperatures of the secondary side, respectively; m h1 and m h2 represent the flow rates of the primary and secondary sides, respectively; c p,h1 and c p,h2 represent the specific heat capacities of the primary and secondary medium, respectively; k he represents the heat transfer coefficient of the heat exchanger; and A he represents the heat transfer area of the heat exchanger. The heat acquired by the heat exchanger is sent to the terminal load. From the point of view of the heat supply network, the heat load can be regarded as a single-port element. The heat load characteristics can be expressed as: , where m represents the mass flow rate of the pipe at the load side, P H,L represents the load thermal power, T L,in and T L,out represent the load inlet and outlet temperatures, respectively. The dynamic model of heat load can describe the change of room temperature in the building. In this article, a first-order dynamic model is proposed to describe the dynamic characteristics of the terminal heat load of the heating system, due to the complexity of the detailed dynamic model of the heat load in the building. Its dynamic model is: where c b represents the specific heat capacity of the air medium in the building, T b represents the equivalent temperature in the building, U b represents the thermal conductivity between the indoor and outdoor environment of the building, T a,b represents the outdoor temperature of the building, T b represents the indoor temperature of the building, P h,r represents the heat dissipation of the radiator in the building, and P h,h represents the heat of other heat sources in the building. The heat dissipation of the radiator in the building is P h,r .
where m ld represents the mass flow of the medium in the radiator pipe, T ld,in represents the inlet temperature of the medium in the radiator pipe, and T ld,out represents the outlet temperature of the medium in the radiator pipe.

Electro-thermal coupling system model
The electro-thermal coupling components mainly include CHP, EB, HP, and circulating pump of heat network system. Different models of CHP have different working modes. The C65 micro gas turbine of Capstone Company is used in this article. The output power of the gas turbine is 23 : where P e,CHP and P h,CHP are the electric power and thermal power output by CHP, respectively, CHP and l are the power generation efficiency and heat loss coefficient of CHP, respectively. The power generation efficiency of CHP is: EB is a device that directly converts electrical energy into heat energy, and its conversion efficiency is close to 1.
where P e,EB and P h,EB are the input electrical power and output thermal power of the EB, respectively. HP is an efficient device for electricity and heat conversion, which is driven by electricity to obtain higher heat energy.
where P e,HP and P h,HP are the input electrical power and output thermal power of the HP, respectively. The circulating pump is used to meet the pressure difference of the supply and return water network by consuming electric energy, and its expression is as follows: where CP represents the efficiency of the circulating pump, m CP represents the flow through the circulating pump, H CP represents the head, and P p,CP represents the electric power consumed by the circulating pump.

Multi-time scale comprehensive model
There are multi-energy coupling and interaction in the electro-thermal system, but the process of its leading effect is different in different time periods. Therefore, the multi-time scale characteristics of the electro-thermal coupling IES can be described in several stages. A multi-time scale comprehensive model of the electro-thermal coupled multi-energy flow system is proposed according to the characteristics of the electro-thermal coupled system, as shown in Table 1.
The models in Table 1 are mainly composed of power system, heating system, and coupling element models. Among them, the dynamic model includes the thermal system and heat load dynamic models of the heating system, and the steady-state model includes the power grid flow model, the coupling element steady-state model, the heat exchanger steady-state model, the hydraulic steady-state model of the heating network, the thermal steady-state model of the heating network, and the heat load steady-state model.
Thermodynamic steady-state model of heating network, Equations (14) and (15) ---√ √ √ Dynamic model of heat load, Equation (5) -----√ --Steady-state model of heat load, Equation (13) -------√ Table 1 does not consider fast dynamic processes, such as the hydraulic dynamic process of the heating network, the dynamic process of the generator in the power system, and the dynamic process of the coupling equipment. At the same time, the dynamic process of the heat exchanger is generally in the time scale of seconds to minutes, and is not considered. Only the thermal process of the heating network and the dynamic process of heat load of minutes and above are considered. Steady-state model 1 is used to analyze the system state on a second time scale; steady-state model 2 is used to analyze the system state on a long-time scale, but the load model is not considered; steady-state model 3 is used to analyze the system in which all equipment reaches a steady state. The quasi-dynamic model 1 is mainly used to analyze the temperature change of the heat supply network and the corresponding power flow and the hydraulic state of the heat supply network. The quasi-dynamic model 2 is mainly used to analyze the temperature change of the heat load and the corresponding power grid and heat network state.
The essence of electro-thermal coupled multi-energy flow steady-state analysis is to solve nonlinear algebraic equations, and the essence of quasi-dynamic analysis is to solve partial differential-differential-algebraic equations. The electro-thermal coupled multi-energy flow system needs to establish an iterative strategy between the two systems, and then conduct a comprehensive analysis of the multi-energy flow system. In this article, a global iterative-local simultaneous solution strategy is proposed, and its iterative process is shown in Figure 2.
In Figure 2, x e represents the variable of the power system; x h represents the variable of the heating system; x ec represents the variable of the coupling element in the power system; and x hc represents the variable of the coupling element in the heating system. Among them, the global iteration is used between different control centers and processes, while the local iteration is only used for calculations in the same control center and the same process.
Each control center only calculates the responsible energy flow system, and then sends the variables of coupling elements to other control centers. In order to simplify the iterative calculation, this article puts the coupling element calculation into the heating system for calculation, and the iterative strategy is shown in Figure 3.
Using the iterative strategy of Figure 3 can keep the original calculation program of the power system unchanged, and the two control centers only interact with the variables of coupling elements in the power system. The iterative strategy shown in Figure 3 can realize that the power system control center and the heating system control center can simultaneously obtain the coupling element model by establishing the input and output model of the coupling element. The multi time scale comprehensive analysis process of electric-thermal coupling is shown in Figure 4.
The calculation process in Figure 4 includes two iterative processes: the iteration between the thermal system and the hydraulic system, and the iteration between the heating system and the power system. In the steady-state analysis, one simulation period can be set. In the process of dynamic calculation, if there is no initial value, the steady-state value is obtained by steady-state calculation, and the steady-state value is used as the initial value for dynamic calculation.

ELECTRO-THERMAL COUPLING INTERACTION AND FAULT PROPAGATION
Coupling is the cause of the interaction. In this article, the interaction of electro-thermal coupled multi-energy flow system is analyzed from four aspects of source, network, load, and storage. On the source side, it is mainly composed of coupling elements such as CHP, HP, and EB, which are used to realize energy conversion. The operation mode of coupling elements has a great influence on the operation of power system and heating system. On the network side, the coupling is mainly composed of control devices such as circulating pumps or valves to regulate and control energy, but the faults of these devices lead to further propagation through network coupling. On the load side, there is a coupling relationship between electro-thermal loads through correlation and complementarity. On the energy storage side, the electro-thermal energy storage has a coupling relationship through the market information of electricity price and heat price.
For the electro-thermal coupled multi-energy flow system, the interaction is analyzed through three links, including disturbance, propagation, and response. The disturbance is mainly represented by the change of non-active control, such as load fluctuation, component failure and so forth. Propagation is mainly concerned with the propagation of disturbances between systems. In order to facilitate analysis, the coupling element is equivalent to a two-terminal component connecting the power system and the heating system, and the input and output of the two systems are P A and P B , respectively, the propagation characteristics are described by the relationship between P A and P B . When P A increases, P B also increases, indicating a positive correlation between P A and P B . When P A increases, P B decreases, indicating a negative correlation between P A and P B . When P A increases or decreases, P B does not change, which means that P A is independent of P B , that is, the two systems are completely decoupled. The response is that after the disturbance propagates, the change of other variables in the system causes the response of the whole system.
The schematic diagram of the interaction mechanism of the electro-thermal coupled multi-energy flow system is shown in Figure 5.
In the process of coupling, the dominant process of different time scales is also different, so the characteristics of different time scales are also different. In the short time scale of seconds, disturbance mainly affects the power flow distribution of power system and the hydraulic condition of heat network. In the middle time scale of minute scale, disturbance mainly affects the temperature distribution of heat network. In the long time scale of hour scale, disturbance mainly affects the temperature of load. In the electro-thermal coupled multi-energy flow system, the fault of the power system will spread rapidly in the power system, but when the fault propagates to the heating system, it will affect the propagation process of temperature in the pipeline and the change of load temperature. The final impact may take several hours or even 10 of hours.
With regard to the interaction strength after electro-thermal coupling, it is proposed to use the comprehensive sensitivity to characterize it. The greater the comprehensive sensitivity, the stronger the interaction intensity, which can be expressed as: where X is generally the variable corresponding to the disturbance, and Y represents the variable to be monitored.
In steady-state analysis, the sensitivity can be calculated by Jacobian matrix in the process of solving multi-energy flow. For the dynamic process of heating system, it is difficult to obtain fixed sensitivity by analyzing the dynamic process of interaction based on simulation. The interaction is realized by coupling for the electro-thermal coupled multi-energy flow system. Therefore, solving the sensitivity between the two systems can be divided into several parts, which can simplify the solution process, as follows: For Equation (22), the specific solution process is as follows: Step 1: Solve the sensitivity of variable Y to the input/output variable Z Y of the coupling element Z in the system where variable Y is located; Step 2: Solve the sensitivity of the input / output variable Z Y of the coupling element Z in the system where the variable Y is to the input / output variable Z X of the coupling element Z in the system where the variable X is located; Step 3: Solve the sensitivity of the input/output variable Z X of the coupling element to the variable X in the system where the variable X is located; Step 4: The coupling sensitivity S YX is calculated according to the results of steps 1, 2, and 3.

F I G U R E 5 Schematic diagram of electro-thermal coupling interaction mechanism
For the electro-thermal coupling IES, the sensitivity of the power system and coupling elements is relatively simple, while the heating system is difficult to obtain a fixed sensitivity in general due to its strong nonlinearity and diversity of control modes, and the sensitivity value is closely related to the operating state of the system. At the same time, the heating system also has a slow dynamic process. To analyze the dynamic process of interaction, it is necessary to analyze the response process of disturbance fault based on the method of simulation. Compared with sensitivity analysis, the most important parameter in the dynamic analysis process is the response delay, that is, how long does it take for variable Y to respond after variable X changes.
As a subset of the disturbance, the fault has a great influence and poses a great threat to the normal operation of the electro-thermal coupled multi-energy flow system. Fault propagation is a special case of interaction, which propagates between power system and heating system. When the power system fails, it will lead to a local power outage, which in turn leads to over-limits or faults in the heating system, such as power outages in the power system causing circulating pumps, heat pumps, electric boilers, solenoid valves, and other equipment to be unable to work, resulting in the whole or part of the heating system cannot work, resulting in the heating system affected. When the heating system fails, it will change the electric output of the coupling element or change the electric load, which will have a certain impact on the power system. There is an essential difference between the fault propagation of electro-thermal coupled multi-energy flow system and that of simple power system. The fault propagation of electro-thermal coupled multi-energy flow system evolves at different time scales. A fault may lead to a new fault several hours or even 10 of hours later, so that the fault propagation analysis needs to cover a longer time. For example, after the failure and shutdown of the heating system, it will take several hours for users to feel the change of load temperature, and then use of electric heating equipment such as air conditioners. And with the passage of time, the demand for electric heating load is increasing, which leads to local overload in the power system, and will cause power system failure in serious cases.

EXAMPLE ANALYSIS
In order to analyze the interaction mechanism between electro-thermal coupling IES, typical scenarios are analyzed and calculated by means of arithmetic examples. At present, CHP is still used as the main electro-thermal coupling element in practical engineering applications. For this reason, the example first uses CHP as the coupling element to analyze through the simple electro-thermal coupling IES, and then adds the coupling element and uses the complex system to analyze. The use of simple systems is helpful to understand the interaction process of electro-thermal coupling and summarize the law, which can further analyze complex systems. In order to fully analyze the interactions between electro-thermal coupling IES, several scenarios are used for analysis, as follows:

Influence of heat load output disturbance on power system
During the normal operation, the increase of heat load is taken as a disturbance to analyze the impact on the power system. In this article, a simple electro-thermal coupled multi-energy flow system is used as an example for analysis, the specific wiring diagram is shown in Figure 5. The power system consists of a synchronous generator G1, three nodes, and three electrical loads, and the three electrical loads are L 1 = 2, L 2 = 1, and L 3 = 2 MW. The heating system consists of a heat source and a heat load. The coupling element is CHP, which is used as the power source of the power system and the heat source of the heating system. In the power system, G1 is used as a balancing machine, and the thermoelectric output characteristics of CHP are shown in Figure 6. In the heating system, the water supply pipe and the return water pipe are symmetrical, the pipe diameter is DN250, the length is 1000 m, and the pipe resistance coefficient is 0.5. The electric load adopts the thermal power model, and the water supply temperature remains constant at 100 • C, while the return water temperature in the heat supply network decreases with the increase of the heat load. In order to meet the demand of the heat load, the heat load is met by adjusting the flow rate. The simulation step of 6 min is used in the example, and the simulation time window is 4 h. The heat load increases once an hour, followed by 2, 3, 4, and 5 MW. The electric load consumed by the circulating pump in the heating system is directly provided by CHP.
The specific diagram is shown in Figure 6. The thermoelectric characteristic curve of CHP is shown in Figure 7.
The changes of heating system and power system parameters with the increase of heat load are analyzed according to the CHP thermoelectric characteristic curve shown in Figure 7. Among them, Figures 8-10 give the specific changes of the parameters of the hydraulic and thermal circuits of the heating system, respectively. When the heat load increases, the heat load terminal meets the demand of the heat load by adjusting the pipe flow of the heat network and reducing the return water temperature. The return water temperature of CHP does not respond to the change of load return water temperature in time due to the time delay of return water pipeline. With the increase of mass flow, the pipeline transmission delay decreases gradually. Because the return water temperature of CHP does not decrease in time, the heat output of CHP increases while the mass flow rate increases. After the transmission delay, the return water temperature of CHP decreases, causing the return water temperature difference of CHP to increase, while the mass flow rate does not change and the heat output of CHP increases once again. According to the constant total output of CHP, with the increase of heat output, the electric output also increases accordingly. In order to meet the electric load demand of the power system, the output of the generator unit G1 is reduced accordingly, which in turn leads to the change of the power flow distribution of the power system, as shown in Figure 11.
As can be seen from Figure 11, the change of heat load has a certain impact on the power distribution of the power system. With the increase of heat load, the power output of CHP increases gradually, resulting in a corresponding decrease in the output of generator G1, which in turn leads to great changes in the power distribution of power system lines. Therefore, the change of heat load in the electro-thermal coupled multi-energy flow system of the park will have a certain impact on the safety and reliability of the power system.

Influence of electric load output disturbance on heating system
During the normal operation, the impact on the heating system is analyzed with the power fluctuation of the power supply system as the disturbance. At present, a high proportion of renewable energy is connected to the electro-thermal coupled multi-energy flow system has become an inevitable trend. For this reason, the G1 synchronous generator set is replaced by wind-PV hybrid power generation system, in which the wind and PV power generation is all 2.5 MW, the specific output curve is shown in Figure 12. Figure 12 shows the wind power and PV output data of a region in northern China from 10:00 to 14:00 in winter with a resolution of 15 min. As can be seen from Figure 12, the fluctuation of wind power output power is large, but the fluctuation of PV output data is stable. Meanwhile, the demand for heat load decreases gradually during this period, and the order of each period is 3, 2.5, 2, and 1.5 MW. The calculation step of 5 min is used in the following calculation process and the electric load is kept constant since the data acquisition resolution of wind and PV power output is 15 min. Figures 13 and 14 show the changes in the parameters of the heating system and the power system, respectively. As can be seen from Figures 13 and 14, due to the influence of CHP thermoelectric characteristic curve and un-adjustable wind and PV output, the normal operation of the power system can be ensured by adjusting the return water temperature and pipeline flow of the heating system. While ensuring the heat load demand, the power balance of the power system is realized and the operation reliability of the power system is improved. For example, due to the fluctuation of the wind-PV power output, the power balance is adjusted by CHP, but restricted by the heat-electricity ratio of CHP, the thermal power output of CHP may be larger than the heat load power or less than the heat load power. By adjusting the pipe flow rate and return water temperature, the heat load demand of the heating system can be met in advance to ensure the power balance of the power system. Meanwhile, the heating system can be regarded as an energy storage system to realize the power adjustment of the electro-thermal coupling system. Through the interaction of CHP coupling elements and electro-thermal coupling system, the power complementarity of electro-thermal coupling multi-energy flow system is realized and the operation reliability of electro-thermal coupling system is improved.

Analysis of fault propagation process in electro-thermal coupling integrated energy system
Electro-thermal coupled multi-energy flow system fault propagation. The Barry Island electro-thermal coupled multi-energy flow system is used as an example to analyze the fault propagation process. The system wiring diagram is shown in Figure 15, and the specific parameters of power system and heating system are shown in Reference 21. In this example, the electricity and heat energy output of the three CHP are supplied to the resident users in the same area. Meanwhile, the power system is connected with the public power grid to ensure the reliability of power supply. In Figure 15, the power system and the heating system are separated for easy visualization, while in practice they are located in the same area, which is hereby illustrated.
In the heating system, each heat load represents a heat exchange station. Each heat exchange station is composed of heat exchanger, radiator, and building heat load. For the Barry Island electro-thermal coupled multi-energy flow system, it is assumed that the CHP1 is permanently out of operation due to power system equipment failure. The load of the power system is supplied by the power grid, the heat load of the heating system is provided by CHP2 and CHP3 at full power, and the insufficient part is provided by users using electric heating devices. It is assumed that the load temperature is 20 • C, the efficiency of electric heat transfer is 1, and the thermal conductivity of the building is 0.85 W/m⋅K. The simulation time is 24 h, the simulation step is 30 min and the outdoor temperature change for 24 h is shown in Figure 16. After CHP1 is out of operation, both CHP2 and CHP3 operate in the state of maximum heat output, and the effluent temperature is kept constant at 100 • C. Assuming that there is only a single form of heat energy source provided by the CHP heating network on the heat load side. After the CHP1 is out of operation, CHP2 and CHP3 are also unable to meet the heat energy demand of the load side, which will inevitably lead to a decrease in the temperature on the load side. Taking the CHP1 unit out of operation at the moment of 0, and the temperature inside the building at each load point from 0-24 h is shown in Figure 17.
As can be seen from Figure 17, the indoor temperature of the building gradually decreases over time, and the lowest temperature decreases to 11 • C for load node 20. At the beginning of CHP1 withdrawal from operation, due to the existence of the time delay in heat transfer from the heating system pipes, the temperature of all load nodes is within the standard heating temperature range, that is, above 18 • C. However, as time passes, and the outdoor temperature also gradually decreases, when 5 moments, there is a load node in the heating system where the indoor temperature is below 18 • C; when 9 moments, the indoor temperature of all load nodes in the heating system is lower than 18 • C, the whole heating system cannot meet the standard of heating temperature. Especially after 18 moments, the temperature on the user side decreases further with the sudden drop of outdoor temperature.
Therefore, after the fault disturbance of the electro-thermal coupling IES, due to the slow dynamic process of the heating system, the heating system will not respond until 4 h and 45 min after the power system fails. The heating system has poor sensitivity, which is essentially different from the sensitivity response of the power system.

F I G U R E 19 Electric load change
When the CHP1 is out of operation and cannot meet the needs of heating users, it is assumed that there are electric heating devices on the user-side to ensure that the temperature in the building meets the heating requirements. By adding an electric heating device on the user-side, the indoor temperature of the building at each load point from 0-24 h is shown in Figure 18.
As can be seen from Figure 18, the temperature in the building can all meet the requirements by accessing the electric heating device, and the lowest temperature is 18.1 • C. At this time, the electrical load of the power system increases significantly. At the beginning, the electrical load basically does not change because the temperature of the heat load does not change much, but as the temperature in the building decreases, the electrical load begins to increase. As the temperature inside the building is also affected by the outdoor temperature, the electrical load also changes with the outdoor temperature, as shown in Figure 19.
As can be seen from Figure 19, the withdrawal of CHP1 from operation leads to an increase in all loads in the power system, especially L1, which increases by 1 MW, resulting in an aggravation of the line transmission power as well. If the outdoor temperature drops further, the electrical load will further increase, which in turn may lead to the withdrawal of power system equipment from operation due to overload, making the fault range will be larger, and seriously affect the safety and stability of the electro-thermal coupling IES.

CONCLUSIONS
The main conclusions obtained in the article are as follows: 1. When the heat load demand increases, the heat demand of users can be guaranteed by increasing the flow rate of heat network pipes and reducing the return water temperature due to the large inertia of heat transfer in the heating system. He has compiled more than 20 planning reports. He published 3 core papers in Chinese and authorized 7 patents. His research direction is power grid planning.
Xiaoqing Hao was born on September 29, 1986 in Hohhot, Inner Mongolia Autonomous region. In 2009, he received a bachelor's degree in electrical engineering and automation from Inner Mongolia University of Science and Technology. In recent years, he has been engaged in the research work in the field of lightning protection detection of renewable energy power station and comprehensive utilization of renewable energy. In the field of electro-thermal coupled multi-energy flow system, there are many demonstration projects. Two academic papers were published and two patents were authorized.