Operation optimization of integrated energy systems based on heat storage characteristics of heating network

With the development of multi‐energy technology, the electric‐heat integrated energy system has become an important research direction for multi‐energy joint supply. The dynamic characteristics and energy storage capacity of heat supply network provide potential for joint dispatching of electric heating energy system. Aiming at the problem of electric‐heat joint dispatching, this paper presents an operation optimization model of electric‐heat integrated energy system considering the virtual energy storage characteristics of heat supply network. Firstly, according to the characteristics of transmission delay and user temperature fuzzy, the virtual energy storage characteristics of heat supply network are studied, and a model of the dynamic transfer of energy in the heat system was built. Then, the operation optimization model of the electric‐heat integrated energy system is established to minimize the operation cost. In order to improve the robustness of scheduling optimization results, the Monte Carlo Simulation embedded Quantum Particle Swarm Optimization algorithm is proposed to solve the model. In order to prove the validity of the proposed model, this paper selects a park (a 36 node thermal system) in the northwest region of China as a simulation case. The results show that the operation optimization method considering the virtual energy storage of heat supply network will greatly enhance the complementary potential of the electric‐heat integrated energy system and reduce the operation cost of the system.

(IES) as the physical carrier of energy Internet has gradually attracted the attention of relevant scholars. 4,5 To enhance the energy supply capacity of the energy system and reduce the cost of energy supply, some scholars have integrated the power system and the heat system, and established different forms of electro-heat coupling structure. Ref 6 proposed an electro-heat coupling model that takes into account the constraint of heat exchange link. Ref 7 analyzed various coupling units such as cogeneration, gas turbine, gas boiler, compressor, and water pump, and proposed an electro-heat coupling model of limited information interaction between networks. Ref 8 proposed an electro-heat coupling model of the overall energy flow based on the energy balance characteristics and the irreversibility of heat transport. Ref 9 proposed an electro-heat coupling model that takes into account the transmission losses of networks. Ref 10 proposes an extended planning model of multi-energy system integrating active distribution network, natural gas network, and energy hub. Ref 11 proposes a coupling that considers transportation, natural gas, and active distribution network. The above-mentioned study is aimed at connecting the electric and heat systems by establishing a medium (equipment) for the conversion of electric and heat energy.
In the field of operation optimization of IES with electro-heat coupling, Ref 12 proposed a control strategy for Combined Cooling Heating and Power (CCHP) units based on the adoption of energy hubs. Ref 13 proposed a long-term model of multiregional cogeneration and interregional power transmission. Ref 14 proposed an overall energy flow model based on the analysis of the energy and heat transport laws in IES. Ref 15 established energy network equations, generalized Kirchhoff's law from electric network theory to generalized Kirchhoff's law suitable for energy network modeling, and derived generalized concentrated parameter equivalent transport equations. Ref 16,17 constructed an electro-heat coupled network model and proposed an electro-heat mixed tide calculation model. The above Ref on the conversion relationship of energy flows is only applicable to static analysis, and further research is needed on the dynamic conversion of multi-energy flows.
Some scholars have also studied the thermal inertia of thermal system in the optimal operation of the electro-heat IES. Ref 18 studies the electric-heat joint scheduling strategy of the distributed and coordinated control of the thermoelectric unit, the electric heating device and the energy storage device. Ref 19 proposed a multi-time scale energy coordination optimization method considering the variability of response speed in the energy flow change of the heating system. Ref 20 proposed a virtual energy storage system model based on the heat storage properties of the park heat energy. In the above study, the thermal inertia of thermal system is considered in the optimization of IES operation. However, the existing optimization scheduling model of electric-heat coupled IES often focuses on the use of thermal inertia service grid of thermal system to improve the permeability of renewable energy, without considering the incentive mechanism of virtual energy storage in the heat grid for demand response planning.
At present, although there is now research on the virtual energy storage characteristics of the district heat network, the electric-heat IES is still more independent of each subsystem, but rarely considers the temperature dynamic characteristics and heat storage capacity of the pipes in the electric-heat IES heat network, making the heat storage capacity of the electric-heat IES heat network is not fully reflected and utilized. In order to bridge this gap, this paper proposes a heating network model that takes into account the latency of the heat transfer process and the virtual energy storage characteristics of the primary heat network from the temperature dynamics of the district heat network, and establishes an electro-heat IES optimization scheduling model that takes into account the heat transfer dynamics characteristics. In this paper, the temperature of circulating water is adjusted without changing the number and flow of pipe network, the heat storage capacity of heat network is optimized, and the hydrological and thermal control decoupling of regional heat network system is realized. In addition, the Monte Carlo Simulation embedded Quantum Particle Swarm Optimization (MCS-QPSO) algorithm is proposed according to the characteristics of the model in this paper.

AND DYNAMIC MODELING OF REGIONAL HEAT NET WORK S
The virtual energy storage function of the heat network is complex, contradictory and dynamically changing. Modeling the dynamic processes of heat transport is key to reflect the latency and virtual energy storage characteristics of the heat network, which is helpful to the development of energy storage potential of the heat network and to participate in the optimal operation of electro-heat IES.

| Characterization of heat transfer
The traditional energy system is limited to a single form of energy dispatch, such as electricity and heat, which does not take advantage of the complementary advantages of different energy sources. An IES can combine energy supply, energy conversion, energy storage, energy consumption, and other physical processes into a unified energy supply system. The electric-heat IES combines the original independent electric and heat systems, which makes the whole system highly complementary. In the electric-heat IES, the power system mainly includes cogeneration units, photovoltaic panels, wind turbines, distribution grids, etc, who are responsible for the supply and transmission of electricity in the entire system. The heating system includes cogeneration, electric boiler, heat exchange station, and heat network to meet the needs of users. The transmission of electric energy in the power system has the characteristics of real-time, fast and strong balance, and the storage of electric energy has the disadvantage of high cost and difficult storage. The heat transfer dynamics are described on a time scale of seconds, minutes, or even hours, and are characterized by easy storage, difficult transmission, and transmission delays. And there is a certain ambiguity in the user's requirements for heat load. Therefore, the heat load has tunable properties over the electric load in terms of amplitude, a certain degree of panning in the timeline, etc In addition, equipment such as cogeneration and electric boiler convert other energy sources into heat, coupling the electric and heat systems. As a result, integrated electric heating energy systems have strong complementary characteristics in energy production, energy supply, energy consumption, etc A typical heat system is shown in Figure 1, it mainly composed of 4 parts: heat source, heat grid, heat exchange station and heat load. 20 Similar to electric systems, heat systems can be divided into transmission systems (primary pipeline network) and distribution systems (secondary pipeline network). 19 The physical network of the primary and secondary pipelines is not connected, but heat exchange is carried out through heat exchange station. A heat exchange station is a heat load in the transmission system and a heat source in the distribution system. There are two main important features of the heat transfer process, as shown in Figure 2 i) Latency of transmission. The transfer of heat energy from the production facility to the user takes a certain amount of time, and changes in heat production are not immediately reflected on the user side.
ii) Ambiguity of heat sensation. A change in room temperature over a certain period of time will not affect the user experience and satisfaction.
Currently, the heat system calculates the temperature setting value for the secondary pipeline network water supply based on the outside temperature and the outside temperature compensation curve. Each heat station is reasonably set according to this value, and the electric valve on the primary pipe network is adjusted to achieve automatic flow or temperature regulation. This mode of operation achieves a balance between supply and demand for fixed heating delay times. Since the dynamic process of heat energy transfer has a large time scale, the heat of hot water entering and leaving the pipeline may not be equal at the same time, and the heat network can play the role of buffering energy and delaying the response, 21 thus exhibiting the characteristics of virtual energy storage and recharge similar to energy storage systems. Considering the delayed and fuzzy of heat transfer, in the low price period, the heating facilities increase the power generation. The system controls the heat flow to each heat exchange station by regulating the electric valve, so that the heat is stored in the primary network. This mode of operation effectively takes advantage of the underestimation of electricity prices and the delay in the transmission of heat energy, enabling the transfer of heat energy across time.

| Kinetic model of heat transfer in heating pipes
The dynamic characteristics of heating pipes refer to the coupling relationship between the hot water inlet temperature and outlet temperature in the same pipe and its time, which is the key to describe the heat storage characteristics of the heating network. In a pipe, the change in water temperature at the inlet will slowly extend to the outlet, and the delay in temperature transfer will be essentially the same as the time the hot water flows through the pipe. In addition, due to the difference between the hot water temperature in the pipe and the ambient temperature, there will be heat loss during the flow resulting in a drop in water temperature. The cross-section of

Thermal Load
Secondary Pipe Network the heating pipe is shown in Figure 3, where Δt is the length of the scheduling period.
Assume that the time required for hot water to travel from inlet to outlet in pipe k is k,t and there is no heat loss in between, then Equation (1) indicates that the discharge temperature T out′ k,t of pipe k at time t is equal to the inlet temperature T in k,t− k,t at time t − k,t when heat loss of the pipe is not considered; the characteristic quantity Y k of pipe k in Equation (2) is determined by parameters such as pipe length and cross-sectional area.
Calculate the effect of heat loss during transmission, as shown in Equation (3) The upper equation can be approximated as: where T w,t is the ambient temperature of the pipe; is the heat conductivity of the pipe material; and L k is the length of the pipe k.
During a scheduling period, if the heat source heat output is greater than (less than) the user's heat demand, the heat network virtual energy storage system plays an energy storage (or discharge) role, which is reflected by the return water temperature increases (or decreases) compared to the previous period. High return water temperature of the heat network will lead to an increase in heat network losses, while too low return water temperature will affect the heat transfer effect between the first and second heat network.
where T return is the return water temperature of the first heat exchanger station, °C; T return max is the upper design limit of pipeline return water temperature, corresponding to the upper limit of heat network energy storage; T return min is the lower design limit of pipeline return water temperature, corresponding to the upper limit of heat network energy discharge; the greater the difference between T return max and T return min , the stronger the heat network energy storage capacity.

| Nodal energy dynamic model
Temperature regulation and flow regulation are two modes of regional heating network operation. In this paper, the temperature regulation method is used to control the temperature of the water supply and return, so as to control the energy in the heating network. And IES primary heat network structure diagram is shown in Figure 4.
(1) Nodal flow balance That is, node mass flow continuity, so that the inflow of hot water into each node equals the outflow of mass flow, the specific expression is where d in l,n represents the medium flow from branch n to pipe section l; d out l,m represents the medium flow from section l to branch m; n and m are the number of branches flowing in and out of the medium, respectively.
(2) Pressure loss balance The pressure loss in the pipeline is divided into the loss along the pipeline and the local loss. The loss along the pipeline is the pressure loss when the pipeline state is unchanged. Local loss is the pressure loss when the pipeline state changes.
where Δg f is the pressure loss along the pipeline section l; Δg j is the local pressure loss of pipe section l; and are the pressure loss coefficient of the resistance along the pipeline and the local resistance, respectively; d is the flow through pipe l; r is the radius of pipe l; g is the acceleration of gravity.
In order to ensure the normal flow of medium in the pipeline, the lost pressure should be supplemented by the pump.
where g p is the pressure provided by the electric boiler.
(3) Heat energy balance The energy contained in the flow of medium into and out of a certain pipe section is constant.
where Q in l,n is the energy carried by the medium when it flows into the pipe section l; Q out l,m is the energy carried by the medium when it flows out of the pipe section l; c s is the specific heat capacity of the medium, kJ/(kg °C); is the density of the medium.
(4) Heat exchange station model For the first station of heat exchange in the primary heat network, the load and loss can be bound together to become the calculated load of the first station of heat exchange, replacing the user load and the heat loss of the heat exchanger and the secondary heat network in the model, following the concept of calculated load in power system analysis. The first heat exchange station model in this paper is: where Q ,j is the period load at the first station of heat exchange, kJ; w ,i is the mass of hot water flowing through the first station of heat exchange at load i in time , kg; T supply ,i and T return ,i are the temperature of water supply and return water at the first station of heat exchange at period , respectively, °C.
The heat exchange station acts as a connection between the primary and secondary heat networks by regulating the flow in the pipes of the secondary heat network to specifically meet the user's heat load requirements. The relationship between heat exchange station heat exchange and heat load is: where Q load ,i is the calculated heat load of the heat exchanger station at load i in time , kW.

| Objective function
The main goal of electro-heat IES optimization scheduling that takes into account the dynamic characteristics of heat energy transport is to minimize the operation cost of electro-heat IES while meeting the electric and heat load demands of the users. Operation cost includes the electricity purchase cost for the upstream grid and the gas purchase cost and maintenance cost. The objective function of the electro-heat IES optimization scheduling model considering the dynamic properties of heat energy transport as follows.
where C is the operation cost, Yuan; C grid is the power purchase cost, Yuan; C gas is the gas purchase cost, Yuan; C mc is the operation and maintenance cost, Yuan.
where F grid is the electricity price in time , Yuan/kWh; P grid is the power purchased by the system from the upstream grid to meet the load in time , kW; P EB is the power of EB in time ; F gas is the gas price, Yuan/m 3 ; V gas is the volume of gas purchased by the system from the upstream gas grid in time , m 3 ; w i is the maintenance cost of a single unit, Yuan.

| Constrains
(1) Electric power balance constraints where P CHP is the CHP electric power in the period, kW; ∑ i P load ,i is the electric load of load node i in the period, kW; P lost is the electric system network loss in the period, kWh; F is the loss factor, equal to the ratio of the square of the root mean squared current to the square of the maximum current; R is the line resistance, Ω; I max is the maximum load current in the period, A.
(2) Output and state change constraints of the device.
where the subscripts min and max indicate the upper and lower limits of force output, respectively; U CHP max and D CHP max are the limits of CHP's upward and downward climbing rates, respectively. (

3) Electric network transmission constraints
In Equations (29)-(30), P Gi , G Gi , P Li and G Li are the active and reactive power injected into node i by the generator and the active and reactive power absorbed by the load from node i, respectively; U i is the node voltage; ̇I i is node current; A is the set of nodes (m1, m1 ≥ 1) that inject active power relaxation; B is the set of nodes (m2, m2 ≥ 1) that inject reactive power relaxation; D is the set of nodes (m3) specified by the voltage magnitude.
(4) Heat transfer first station constraints where Q CHP and Q EB are the heat power of CHP and EB at time , respectively; w ,m is the mass of hot water flowing through the first heat exchanger station at time .
In order to facilitate the analysis of the virtual energy storage regulation potential of the heat network in the electro-heat IES optimization scheduling, the virtual energy storage, charge, and discharge power of the heat network is defined as where G is the virtual storage and discharge power of the heat network, "storage" is positive, "discharge" is negative; Q is the heat output of the system when considering the dynamic characteristics of heat energy transfer; Q′ is the heat output of the system without considering the dynamic characteristics of heat energy transfer, the heat output of the system under the scheduling scheme should always meet the demand for heat supply.

| Variable identification
The type and quantity of variables will affect the accuracy and time of model solution. Therefore, the variable identification is a key step to realize the accurate solution of the operation optimization model of the IES.
As shown in Table 1, the structure of optimization model is very complex, including many noninteger variables and integer variables. In addition, the coupling between electric network and thermal network is nonlinear. Therefore, the operation optimization of comprehensive energy system is a complex nonlinear optimization problem.

| Solution algorithm
Renewable energy sources such as solar energy and wind energy are an important part of the electron-heat IES. However, the power generation capacity of wind turbines and photovoltaic equipment is highly uncertain. Meanwhile, the load demand of IES is also highly uncertain. The operation optimization problem of electric-heat IES is a typical nonconvex and nonlinear optimization problem. Therefore, Monte Carlo simulation embedded quantum particle swarm optimization (MCS-QPSO) algorithm is proposed to solve this problem.
(1) MCS random power flow processing IES power flow in the distribution network containing renewable energy is stochastic. Therefore, the stochastic power flow method based on MCS is adopted in this paper to solve the power flow of the distribution network with uncertainties included. The basic process is shown in Figure 5 Based on the central limit theorem, the power prediction error and load demand prediction error of renewable energy are usually normally distributed. In the IES operation study, the normal distribution model can be used to represent the wind turbine, photovoltaic power generation, and load demand prediction error. 22 The specific model is as follows: In the formula, ΔP uncertainty is the prediction error of wind turbine, photovoltaic power generation and load demand; the error expectation is 0; 2 uncertainty is the variance. 2)A large number of random data are generated by MCS method to simulate the random output characteristics of DG within an hour. The sampling interval of MCS was 1 hour, and the sampling period was 8760 hours. The random data generated by MCS were substituted into the forward pushback algorithm to realize the random power flow calculation of distribution network with uncertain factors.
(2) Improved Quantum Particle Swarm Optimization (QPSO) Particle Swarm optimization (PSO) is an adaptive evolutionary computing technology based on population search. As an important optimization tool, particle swarm optimization algorithm has been successfully applied to functional optimization, neural network training and other fields. 23 However, like other global optimization algorithms, PSO algorithm also has some problems to be improved in practical application, such as poor global optimization ability, premature phenomenon, and slow convergence rate. 24 The proposed quantum particle swarm optimization (QPSO) is based on quantum evolutionary algorithm into PSO algorithm, the algorithm adopts the qubits to encode the particle's current location, using quantum revolving door to search the best position of the particles, and the variation of particle position implemented with quantum gate to avoid premature phenomenon, and greatly improve the PSO algorithm is global search optimization ability and efficiency of optimization. At the same time, it further strengthens its global search capability by introducing the process of "catastrophe." The main steps of QPSO algorithm are as follows: 1)Quantum coding mode of particles In quantum computing, �0⟩ and �1⟩ are used to represent the two basic states of microscopic particles. They are called qubits, and the symbol "�⟩" is the Dirac symbol. Similarly, in the QPSO algorithm, the smallest information unit is the qubit, which has two basic states-state �0⟩ and state �1⟩. Therefore, in this paper, the probability amplitude of qubits is directly used as the encoding of the current position of particles. Each particle in the population occupies the following two positions in the traversal space, whose probability amplitude of quantum state and �1⟩ is, respectively: In the formula, P In the formula, mn and mn represent the probability amplitude of the dimension of the particle; m and n are solution space variables; x mn and y mn represent the upper and lower limits of particle m's search range.
3)Phase shift in solution space The particle solution space of the QPSO algorithm in this paper converts the spatial phase shift of the particle moving velocity in the basic PSO algorithm into the spatial phase shift of the quantum rotation gate corner, and the spatial phase shift of the particle is converted into the phase shift of the quantum probability amplitude on the particle.
In the formula, Δ (j) mn represents the phase of particle m at the n-dimension in the j iteration; (j) pmn and (j) gn , respectively, represent the historical optimal phase of particle m in the n TH dimension and the global optimal phase of the n TH dimension in the j iteration. cos (j) mn and sin (j) mn represent the n TH dimensional probability amplitude of particle m in the second iteration of j. s 1 and s 2 are acceleration coefficients; is the inertia factor; r 1 and r 2 are random Numbers between [0,1].

4)Mutation operation
The main reason why PSO algorithm is easy to fall into local optimization is the loss of population diversity in the search process. In QPSO algorithm, mutation operation can be realized through quantum nongate, which can significantly increase the diversity of population and effectively avoid premature phenomenon. Its operation process is as follows: In addition, each particle generates r random number A between [0, 1] and compares it with the set probability of variation p b . If r ≤ p b , the probability amplitude of the randomly selected [i∕2] qubits is changed by the quantum nongate, where i is the total number of qubits.

| Solution process
The specific optimization solution flow of economic operation of IES based on MCS-QPSO algorithm is shown in Figure 6. 1. Initialize the model and algorithm parameters. Parameters such as population size, iteration number, sampling number, and normal distribution model were set. 2. QPSO population initialization. Based on the probability distribution of renewable energy output, the renewable energy generation capacity was predicted using historical data and the initial operation scheme of IES was generated. 3. Constraint inspection. The constraints of the access scheme are verified by Monte Carlo simulation. If the condition is met, perform step 4; otherwise, add the fitness of the particle to the penalty term M and proceed to the next step. 4. Space transformation and fitness calculation. According to Equation (31), the solution space is transformed and the positions of randomly generated particles are mapped to the solution space of the problem. According to the objective function formula (14) and the corresponding constraint conditions, the fitness of each particle is calculated to find a single extreme point and a global extreme point. If it is better than the historical extreme, the current extreme is substituted for the historical extreme. Otherwise, update calculator N = N + 1 and proceed to the next step. Record: Record the history and global optimal phase of each particle Update location: Update particle position

Mutations:
Record the probabilities of variant particles select: Select particles to participate in the next iteration.

Compared:
Compare the phase of the best particles and select the corresponding best particles 5. Particle state update and mutation operation. According to Equations (32)-(34), particle state update and mutation operation are realized. 6. Cyclic operation.
Step 3 is returned until the convergence condition is satisfied or the maximum number of iterations is reached. 7. Improve the convergence speed. If the optimal individual cannot be renewed for a long time, the population disaster strategy is adopted to replace the population individual with its historical optimal individual to form a new population. 8. Output the optimal scheme.

| Background
In this paper, a park (36-node heat system) in northwest China is selected as a simulation example. The structure of the 36-node heat network is shown in Figure 7. Among them, the electric and heat coupled devices include the following: CHP located at nodes 1, 13, 17 of the heat network, and an electric boiler (EB) located at node 32 of the heat network.
The total installed capacities of CHP and electric boilers are 70 MW and 90 MW, respectively. Since the time scale of the dynamic process of electricity transmission is much smaller than that of the heat grid, the grid structure is ignored in this paper. At the same time, the size of hot network nodes is increased to verify the effectiveness and robustness of the proposed algorithm MCS-QPSO. In order to prove the validity of this model more clearly in this paper, the example is constructed to compare two typical scenarios: Scenario 1: Electro-heat-IES-operation optimization model without considering the dynamic properties of heat energy transfer. Scenario 2: Electro-heat-IES-operation optimization model considering dynamic properties of heat energy transfer.
The heat output of the energy equipment in Scenario 1 should be equal to the heating demand at all times, regardless of the latency and virtual energy storage characteristics of the heat network, and only the losses of the heat network should be considered. In this scenario, the return water temperature in the first heat exchange station is kept constant, thus ensuring that the heat output of the source-side energy conversion equipment is equal to the charge-side heat demand at each point in time.
In order to respond to the demand response policy in the park, the park needs to optimize scheduling through peak cutting and valley filling, peak shifting operation, etc The electricity price, estimated power consumption, and heat load of a typical day in the park are shown in Figure 8.

| Simulation results
(1) Heat system output comparison Figures 9 and 10 are the results of heat system output under two scenarios. As can be seen from the figures, the heat source heat supply and heat load of the heat exchange station in the heat system in scenario 2 are not synchronized, while scenario 1 is synchronized.
The dynamic properties of heat transfer in Scenario 2 are manifested in the heat system in two ways: 1. At the tariff valley moment, the electric boiler first satisfies the heat load demand, and then exerts more force within the constraints of the virtual energy storage characteristics of the heat network, so as to realize the heat storage of the virtual energy storage of the heat network; then at the tariff level and peak moment, the heat energy stored in the heat network in advance is released to satisfy part of the heat load demand at that time. For example, at 14:00-15:00, the system heat output is significantly higher than the heat load demand, while at 16:00-17:00, the system heat output is significantly lower than the heat load demand. 2. The positive relationship between CHP loading rate and COP can be seen in Figure 11. Based on the time-delay and virtual energy storage characteristics of the heat network, it is firstly possible to increase the output force while the CHP meets the heat load demand, which not only improves the heat efficiency but also saves the operation cost of the CHP at the next moment. For example, in 1:00-4:00 and 21:00-24:00, the CHP in the heat system increases the output force at 1:00, 3:00, 21:00, 23:00, so that the CHP does not output at 2:00, 4:00, 22:00, 24:00; also, in the CHP continuous heat output period, the average COP of CHP can be increased through the CHP preheating output force, for example, in 18:00-20:00, the CHP preheating output force, so that the average COP of CHP at 18:00, 19:00, 20:00 three time points relative increases.
(2) Electricity system output comparison Figures 12 and 13 show the results of the power system output for the two scenarios. Each power supply equipment will reasonably generate electricity during each time period to meet the demand of users and equipment operation. The difference in the electric system output in the two scenarios is synchronized with the heat system. There are two main reasons: First, because of the dynamic characteristics of heat energy transmission in scenario 2, more electricity is purchased to achieve virtual heat storage during the trough of the electricity price, and electric heating is reduced during the price plateau and peak, and the electricity output in scenario 2 is higher than scenario 1 during the trough and lower than scenario 1 during the peak; second, CHP adopts the operation mode of "heat to power", because CHP considers the relationship between the load rate and the COP in the heat system, CHP preempts to increase the average COP of CHP and reduce operation cost, so CHP in the electric system and the heat system synchronize.

| Discussion and analysis
(1) Comparison of energy consumption for different scenarios The power consumption of electric boiler and system gas consumption of the two scenarios are shown in Figure 14. In valley electricity price, in scenario 2, if the electric boiler has space for virtual energy storage, the electric boiler will increase its output, and the power purchase will increase accordingly; if the electric boiler does not have space for virtual energy storage, and because in both scenarios, the electric boiler will give priority to output at that time, which also leads to the same power purchase situation in the figure. In flat and peak electricity price, due to the high cost of power purchase, CHP gives priority to output. Because CHP can meet the demand of heat load in the park, EB output is not required. Thus, the power consumption of electric boiler of scenario 2 is higher than that of scenario 1.
As can be seen from Figure 14, the gas consumption of the system of scenario 2 is significantly lower than that of scenario 1. There are two reasons for this: First, the electric boiler purchases electricity in the valley time, realizing the virtual heat storage; second, the CHP pre output increases its COP.
(2) Cost comparison of different scenarios Based on the conclusion in Figure 12, although the electricity purchase of electric boiler in Scenario 2 is higher than that of Scenario 1, the gas purchase of Scenario 2 is much lower than that of Scenario 1. By comparing the energy cost of the two scenarios in Figure 15 and Table 2, the electricity purchase cost of Scenario 1 is lower than that of Scenario 2, the gas purchase cost of Scenario 2 is lower than that of Scenario 1, and the total operation cost of Scenario 2 is lower than that of Scenario 1. Therefore, F I G U R E 1 0 Scenario 2 optimal dispatch results of heat system 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time/h the advantages of the coordination and complementarity of electric and heat systems are finally reflected by gas purchase cost.
(3) Algorithm validation In addition, the MCS-QPSO algorithm proposed in this paper has the advantage of being fast and accurate in solving large-scale operational optimization problems such as the operational optimization of integrated energy systems. In this section, the performance of the MCS-QPSO algorithm, the genetic algorithm (GA), and the fruit fly optimization algorithm (FOA) are compared in solution 2. It can be seen from Table 3 and Figure 16 that the performance of the MCS-QPSO algorithm is much better than GA and FOA in solving the 36-node hot network structure model.
In order to verify that the MCS-QPSO algorithm proposed in this paper still outperforms similar algorithms in the face of larger network nodes, a 68-node thermal network structure diagram is introduced, as shown in Figure 17. From Table 4 and Figure 18, it can be seen that the GA, FOA and MCS-QPSO algorithms are used to solve the model under the 68-node thermal network structure. The optimal number of iterations for GA is 43 and the calculation time is 45.1 seconds; the optimal number of iterations for FOA is 49 and the calculation time is 50.2 seconds; the optimal number of iterations for MCS-QPSO is 30 and the calculation time is 34.5 seconds. In addition, the optimal cost of the MCS-QPSO algorithm is also the best among the three algorithms. Therefore, when the size of the hot network node structure increases, the MCS-QPSO algorithm is still the best choice for solving the operational optimization model.
In addition, MCS-QPSO algorithm is superior to FOA and GA in calculation results and benefits under 36-node thermal network structure. It can be seen from Table 5 that the global search capability and speed of MCS-QPSO algorithm are not significantly reduced when solving the 68node thermal network structure model. Therefore, the strong global searching ability and robustness of MCS-QPSO algorithm are verified.

| CONCLUSION
In this paper, based on the latency and virtual energy storage characteristics of the heating network, an operation optimization model for the electric-heat integrated energy system is established, which takes into account the dynamic characteristics of heat energy transmission:  analysis of the virtual energy storage characteristics of heat networks. 3. Construct an electro-heat integrated energy system operation optimization model that takes into account the virtual energy storage characteristics of the heat network.

The Monte Carlo Simulation Quantum Particle Swarm
Optimization algorithm embedded quantum gate, revolving door, is adopted to realize the variation of the particle and the search for the optimal position, and the introduction of "catastrophe" process, to further strengthen the global search ability.
Simulation results show that virtual energy storage through the preemptive power of heating equipment not only F I G U R E 1 6 Comparison of iterative curves of different algorithms under 36node hot network structure F I G U R E 1 7 68 node thermal network structure diagram F I G U R E 1 8 Comparison of iterative curves of different algorithms under 68-node hot network structure responds to local time-sharing electricity prices but also saves gas consumption. This achieves a coordinated complementarity between the electric and heat systems in time and space, thus reducing the total operation cost of the system. The next step can be to consider the combination of the three energy conversion device models in integrated energy system, to consider building a dynamic model of the energy transfer dynamics of the cold-heat-electric network, and to explore the coordinated complementarity of the cold-heatelectric system in the space-time range.