Method and system for modeling and simulation of electrical thermal integrated energy system based on holomorphic embedding

Abstract

The present application belongs to the technical field of dynamic simulation of comprehensive energy system, and proposes a modeling and simulation method and system of electrical and thermal comprehensive energy system based on holomorphic embedding, comprising: constructing a dynamic model of a heating network, a dynamic model of a natural gas network and a dynamic model of a power system based on holomorphic embedding respectively; obtaining interface quantities in a mode of determining electricity / gas according to heat; adopting a multi-time-step simulation strategy: advancing the solution of the dynamic model of the heating network at a coarse step to obtain the interface quantities of the power system and the natural gas network, and advancing the solution of the dynamic model of the power system and the dynamic model of the natural gas network at a fine step; based on the advancement of the multi-time-step simulation strategy, recursively solving the coefficients of each order of the dynamic model of the heating network, the dynamic model of the natural gas network and the dynamic model of the power system to obtain the continuous dynamic response of the electrical and thermal comprehensive energy system in the simulation time domain. The present application solves the problems of the traditional discrete coupling solution method in the coordination of simulation accuracy, efficiency and time scale.

Description

Technical Field

[0001] This invention belongs to the field of dynamic simulation technology of integrated energy systems, and particularly relates to a modeling and simulation method and system for integrated electrical and thermal energy systems based on fully embedded systems. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] An integrated energy system (IES) is a comprehensive energy supply system that achieves cross-carrier complementary coupling and cascaded energy utilization by coordinating and optimizing the configuration and scheduling of multiple energy carriers and their conversion equipment within a unified planning and operation framework. On the one hand, IES can improve the overall energy utilization efficiency and system operation economy through multi-energy synergy optimization; on the other hand, relying on multi-source mutual assistance and flexible adjustment capabilities, it can enhance the sustainability and security of energy supply; at the same time, it helps to promote the friendly integration and efficient consumption of renewable energy, and reduce the system's carbon emission intensity.

[0004] Time-domain dynamic simulation is a crucial foundation for the operation analysis, control strategy evaluation, and online verification of the electricity-gas-heat integrated energy system (EGH-IES). Because the transport processes of the natural gas network (NGN) and district heating network (DHN) exhibit significantly slower dynamic characteristics compared to the electric power system (EPS), partial differential equations (PDEs) are typically used to characterize their spatiotemporal evolution. Further coupling with EPS power flow algebraic constraints and the steady-state relationships of coupled equipment can form a large-scale, highly nonlinear system of partial differential-algebraic equations (PDAEs), making it difficult for existing simulation methods to simultaneously achieve both high fidelity and high efficiency.

[0005] For time-domain dynamic simulation of gas / thermal fluid networks, existing research mostly employs the finite difference method (FDM) with spatiotemporal discretization to solve the corresponding PDE. In transient simulation of natural gas pipeline networks, classic works also use discretization and implicit solution strategies to support dynamic calculations of the pipeline network. In general, discretization methods often rely on dense spatiotemporal grids and iterative root-finding solutions, which often require trade-offs between accuracy, stability, and computational cost in engineering applications.

[0006] To avoid the computational complexity issues of discretization methods, scholars have focused on developing more efficient analytical modeling methods in recent years. Typical analytical tools include the Laplace transform, Fourier transform, and the method of characteristics (MOC). Among these, Ma et al. introduced the holomorphic embedding method (HEM) into the unified energy flux solution of IES, providing a new path for "analytical / non-iterative" solutions. Addressing the online / digital twin requirements of IES, Huang et al. proposed a one-dimensional holomorphic embedding modeling and solution framework for IES time-domain simulation and validated it in real-time simulation of an integrated electrical-thermal energy system. However, for integrated time-domain dynamic simulation of heterogeneous electrical-thermal energy systems across time scales, the following key bottlenecks still exist: When dealing with nonlinear and complex boundaries, gas / thermal fluid networks still generally rely on differential discretization and iterative root-finding solutions, which makes it difficult to achieve both high accuracy and high efficiency. In the electrical-thermal coupling scenario, there is an objective time scale difference of 2-3 orders of magnitude between the fast dynamics of EPS (milliseconds to seconds) and the slow dynamics of NGN / DHN (minutes to hours). Traditional discrete coupling usually requires aligning time steps through linear / higher-order interpolation, which introduces additional interpolation errors and increases computational complexity. Summary of the Invention

[0007] To overcome the shortcomings of the existing technologies, this invention provides a modeling and simulation method and system for a fully embedded electrical-thermal integrated energy system. It constructs a time-domain continuous coupling simulation strategy based on the HEM model and realizes cross-time scale information transfer through continuous function / series interfaces, thus solving the challenges faced by traditional discrete coupling solution methods in terms of simulation accuracy, efficiency and time scale coordination.

[0008] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions: The first aspect of this invention provides a modeling and simulation method for a fully embedded integrated electrical and thermal energy system, comprising: Dynamic models of heating networks, natural gas networks, and power systems based on fully embedded systems were constructed respectively. The coupling mode of heat-determined electricity / gas is adopted. The interface quantity injected into the heating network is determined by the state of the heating network side, and the interface quantity injected into the power system and the interface quantity of the natural gas network are obtained by a fixed conversion relationship. The simulation strategy employs multiple time steps: the dynamic model of the heating network is solved under a coarse step size, and the continuous representation of the interface quantities within a certain time window is obtained and mapped to the interface quantities of the power system and the natural gas network, forming continuous function / series interface inputs of the power system and the natural gas network within that time window; the dynamic model of the power system and the dynamic model of the natural gas network are solved under a fine step size. Based on the advancement of the multi-time-step simulation strategy, the coefficients of each order of the dynamic model of the heating network, the dynamic model of the natural gas network, and the dynamic model of the power system are solved recursively to obtain the continuous dynamic response of the integrated electrical and thermal energy system in the simulation time domain.

[0009] As a further technical solution, the construction of a dynamic heating network model based on fully embedded systems includes: Within the time window, two-dimensional spatiotemporal holomorphic coefficients of mass flow rate, pressure, and water temperature in the heating pipeline are defined and reconstructed into a spatiotemporal continuous expression. Substituting the spatiotemporal continuous expression into the hydraulic-thermal dynamic equation of the pipeline and matching the coefficients of the same order, a set of recursive linear equations is obtained. In the recursive forms of the momentum equation and the energy equation, the higher-order coefficients are obtained only by linear calculation of the lower-order coefficients.

[0010] As a further technical solution, the construction of the dynamic model of the heating network based on fully embedded systems also includes: For heating network nodes, the node mass conservation, energy conservation, and temperature mixed constraints are expanded into power series in the time domain, substituted into the node algebraic equations, and the coefficient recursive relationship of the node model is established. Among them, the conservation of nodal mass and energy are given linear constraints at each time order; For the fractional nonlinearity in the nodal temperature mixing equation, a recursive method of finding the inverse of holomorphic functions is adopted. By constructing the holomorphic inverse function of the denominator, the division operation is transformed into a convolution operation, and the power series coefficients of the nodal temperature are obtained.

[0011] As a further technical solution, the construction of a dynamic model of a natural gas network based on fully embedded systems includes: Within a time window, the two-dimensional spatiotemporal holomorphic coefficients of the pressure, mass flow rate, and reciprocal of pressure of the natural gas pipeline are defined in the spatiotemporal domain and reconstructed into a spatiotemporal continuous expression. Substituting the spatiotemporal continuous expression into the partial differential equations for mass and momentum conservation of the pipeline, and using the coefficient domain partial derivative rule and convolution rule, the coefficients of terms of the same power are matched to obtain the coefficient recursive relationship of the natural gas pipeline model. By utilizing the relationship that the product of pressure and its reciprocal is always equal to 1, the recursive relationship of the pressure reciprocal coefficient is obtained by balancing the coefficients of the same power.

[0012] As a further technical solution, the construction of a power system dynamic model based on fully embedded systems includes: Within the time window, the voltage magnitude and phase angle of the bus are expressed as power series with respect to the time-embedded variable, and the active and reactive power injected into the nodes are also expressed as power series. Define the phase angle difference and recursively obtain the power series coefficients of the cosine and sine functions of the phase angle difference; Substituting the power series coefficients into the polar coordinate form of the nodal active / reactive power injection equations and matching the coefficients of the same power, we obtain the coefficient recursive linear equation system of the power system model.

[0013] As a further technical solution, the interface quantities are respectively the thermal power injected into the heating network, the electrical power injected into the power system, and the equivalent load of the natural gas network.

[0014] As a further technical solution, the mapping to the interface quantities of the power system and the natural gas network includes: obtaining the power series coefficients of the interface quantities at the center of the coarse-step long-time window by power series translation, and directly obtaining the input coefficients required for solving the fine-step long-time window.

[0015] A second aspect of the present invention provides a modeling and simulation system for a fully embedded integrated electrical and thermal energy system, comprising: The electrical thermal model building module is configured to: build a dynamic model of a heating network based on full embedding, a dynamic model of a natural gas network based on full embedding, and a dynamic model of a power system based on full embedding. The coupling interface module is configured to adopt a heat-determined electricity / gas coupling mode, determine the amount of interface injected into the heating network based on the status of the heating network side, and then obtain the amount of interface injected into the power system and the amount of interface injected into the natural gas network through a fixed conversion relationship. The multi-time-step strategy configuration module is configured to: advance the simulation strategy with a multi-time-step approach: advance the solution of the heating network dynamic model with a coarse step size, obtain the continuous representation of the interface quantity within a certain time window, and then map it to the interface quantity of the power system and the natural gas network, forming the continuous function / series interface input of the power system and the natural gas network within the time window; and advance the solution of the power system dynamic model and the natural gas network dynamic model with a fine step size. The dynamic response module is configured to: based on the advancement of the multi-time-step simulation strategy, recursively solve the coefficients of each order of the dynamic model of the heating network, the dynamic model of the natural gas network, and the dynamic model of the power system, to obtain the continuous dynamic response of the integrated electrical and thermal energy system in the simulation time domain.

[0016] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps in the modeling and simulation method for a fully embedded integrated electrical and thermal energy system as described in the first aspect of the present invention.

[0017] The fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the modeling and simulation method for a fully embedded integrated electrical and thermal energy system as described in the first aspect of the present invention.

[0018] The above one or more technical solutions have the following beneficial effects: This invention integrates three subsystems—heating network, natural gas network, and power system—into a fully embedded modeling framework, representing their state variables as power series within a time window. By substituting the original partial differential / algebraic equations and matching coefficients of the same power, the original nonlinear equations are transformed into linear recursive relationships in the coefficient domain, avoiding the Newton iteration process in traditional methods and significantly reducing computational complexity. All three subsystems are presented as linear equation systems with recursive power series coefficients, providing a unified analytical interface for subsequent multi-energy coupling solutions.

[0019] This invention establishes a coupled device model and a fully embedded coupled model, which ensures the temporal continuity of energy exchange across networks and avoids the accuracy loss caused by discrete sampling.

[0020] This invention sets different simulation steps for gas / heat networks and power systems by setting a multi-time-step simulation strategy. Each subsystem advances independently according to its own step, which significantly reduces the total number of calculation steps, improves the overall simulation efficiency, and maintains the time domain resolution within each subsystem.

[0021] This invention utilizes a power series translation formula to accurately map the interface quantity coefficients at the center of a coarse time window to the center of a fine time window, achieving "analytical" alignment across time scales, completely avoiding interpolation errors, and maintaining the temporal continuity of the interface quantities.

[0022] The present invention obtains holomorphic coefficients by solving for them, which can directly reconstruct state variables at any time within the time window and obtain the continuous dynamic response trajectory in the entire simulation time domain, providing complete time information for system state perception and control decision-making.

[0023] This invention achieves simulation acceleration while ensuring high precision, and outputs a continuous dynamic response in the time domain, providing key technical support for online verification and real-time scheduling of integrated energy systems.

[0024] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0025] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0026] Figure 1 A flowchart for modeling and simulating the integrated electrical and thermal energy system of the first embodiment; Figure 2 This is a system topology diagram of the first embodiment, EGH-IES-1; Figure 3 The simulation results of the return water temperature at DHN node 1 in the EGH-IES-1 of the first embodiment are visualized. Figure 4 Visual simulation results of CHP thermal output in the EGH-IES-1 of the first embodiment; Figure 5 The results of the visualization simulation of the mass flow rate of NGN node 1 in the EGH-IES-1 of the first embodiment are shown. Figure 6 Visualized simulation results of the pressure at NGN node 7 in the EGH-IES-1 of the first embodiment; Figure 7 Visual simulation results of the voltage amplitude at EPS node 4 in the EGH-IES-1 of the first embodiment; Figure 8 The simulation results of the EPS node 4 phase angle in the first embodiment EGH-IES-1 are visualized. Detailed Implementation

[0027] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0028] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0029] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0030] Example 1 like Figure 1 As shown, this embodiment discloses a modeling and simulation method for a fully embedded integrated electrical and thermal energy system, including: S1: Construct dynamic models of heating networks, natural gas networks, and power systems based on fully embedded systems, respectively. S2: The coupling mode of heat-determined electricity / gas is adopted. The amount of interface injected into the heating network is determined by the state of the heating network side, and the amount of interface injected into the power system and the amount of interface injected into the natural gas network are obtained by a fixed conversion relationship. S3: Employ a multi-time-step simulation strategy: Under a coarse step size, advance the solution to the dynamic model of the heating network, obtain a continuous representation of the interface quantity within a certain time window, and then map it to the interface quantity of the power system and the natural gas network, forming a continuous function / series interface input of the power system and the natural gas network within the time window, and then advance the solution to the dynamic model of the power system and the dynamic model of the natural gas network under a fine step size; S4: Based on the advancement of the multi-time-step simulation strategy, the coefficients of each order of the dynamic model of the heating network, the dynamic model of the natural gas network, and the dynamic model of the power system are solved recursively to obtain the continuous dynamic response of the integrated electrical and thermal energy system in the simulation time domain.

[0031] Specifically: (1) DHN modeling and solution (1.1) PDAE model of DHN (1.1.1) Pipeline hydraulic-thermal dynamic equations For any heating pipeline Establish spatial coordinates starting from the pipeline inlet. The pipeline state quantity is selected as mass flow rate. ,pressure With water temperature Considering the incompressibility of water as an equivalent description of hydraulic transients, and the effects of frictional resistance and external heat dissipation, the one-dimensional dynamic process of a pipe can be represented by the conservation of mass, momentum, and energy:

[0032]

[0033] (1) In the formula: Number the pipes; For spatial coordinates, For time; This refers to the cross-sectional area of ​​the pipe. The density of water; Specific heat capacity at constant pressure; Water temperature; The equivalent heat dissipation coefficient per unit length; This is the equivalent coefficient of friction resistance (related to parameters such as resistance coefficient and pipe diameter); The ambient temperature is used. Furthermore, due to the incompressible nature of water, flow rate and pressure can be considered as instantaneous response quantities.

[0035] (1.1.2) Nodal conservation and mixed constraints A DHN (Deep Hybrid Network) consists of multiple pipes connected at nodes. In addition to the distributed parameter equations within the pipes, the nodes must also satisfy constraints such as mass conservation, energy conservation, and temperature mixing. Let the set of nodes in the DHN be... The pipeline assembly is For any node Define a signed node-pipeline association matrix. : (2) In the formula: The node-pipeline association matrix; For node indexing; Number the pipeline.

[0036] make Collect the mass flow rate of each pipe port (by (The sign convention is positive or negative). , Let the node injection and node demand quality flow vectors be the node injection and node demand quality flow vectors, respectively. Then the node quality conservation is: (3) In the formula: Port quality flow vector; Inject the quality flow vector into the node; This represents the node's required quality flow vector.

[0037] The conservation of nodal energy can be represented by the heat power flow at the ports, and the energy conservation can be written as: (4) In the formula: For port temperature vectors; The node's heat extraction power (a positive value indicates heat extraction from the network). Provide heating power to the nodes; This represents a diagonal matrix composed of vector elements.

[0038] When multiple branches converge at a node, the node mixing temperature can be obtained by weighting the inflow heat flux. For any node... Its mixing temperature can be written as: (5) In the formula: For inflow node The set of branches; , branch road At the node Port flow and temperature; , Inject flow and temperature into the outside of the node (if no injection occurs, take...). ).

[0039] (1.2) DHN Modeling and Solution Based on HEM (1.2.1) Definition of holomorphic embedding and two-dimensional spatiotemporal holomorphic coefficients In the time window Inside, order and with As the current time window expansion center, the pipeline state variables are considered as... The holomorphic functions are defined with two-dimensional spacetime holomorphic coefficients as follows:

[0040] (6) (7) In the formula: For spatial order; For time order; , , These are the two-dimensional spatiotemporal pure coefficients for mass flow rate, pressure, and water temperature, respectively.

[0042] Accordingly, pipeline variables can be reconstructed into a spatiotemporally continuous expression within this window:

[0043]

[0044] (8) In the formula: and These are the spatial and temporal truncation orders, respectively.

[0046] (1.2.2) Holomorphic recursion of pipe segment equations Substituting equation (8) into mechanism equation (1), and applying equations of the same order... By matching the coefficients, a set of recursive linear equations (of various orders) can be obtained. It is only related to lower-order coefficients), thus avoiding Newton iteration on the original nonlinear equation. have to: (9) In the formula: The holomorphic coefficient is defined by equation (6).

[0047] To ensure that the friction term remains analyzable within this time window, let If the sign of the constant is determined by the direction of flow from the starting point of the time window, then the momentum equation can be recursively derived as follows:

[0048] (10) In the formula: This refers to a fixed flow direction symbol within that time window; These are the holomorphic convolution coefficients of the quadratic nonlinear term (which can be calculated using low-order coefficients).

[0050] Similarly, the energy equation is recursively derived as follows:

[0051]

[0052] (11) In the formula: The symbol for Kronecker; For holomorphic convolution coefficients of the convection term; It is the equivalent heat dissipation coefficient per unit length.

[0054] (1.2.3) Holomorphic embedding processing of node algebra constraints Nodal mass conservation and energy conservation at every time order The linear constraints are given above:

[0055] (12) In the formula: Indicates the time order coefficient; These are the known terms obtained from the lower-order coefficients. Depend on The convolution terms below order are summed.

[0057] For the nonlinearity of the mixed temperature fraction in equation (5), a recursive method of "inverting" a holomorphic function is used: let the denominator be...

[0058] (13) Then there is and to Recursion: (14) In the formula: The denominator of equation (5); It is its holomorphic inverse function.

[0060] like For the molecule of formula (5), thus The coefficients of each order can be obtained by convolution, avoiding the need to directly solve by nonlinear division.

[0061] (1.2.4) Time-domain continuous deconstruction Once the holomorphic coefficients of each pipe and each node are obtained, equation (8) can be used to apply the holomorphic coefficients to any... Direct Refactoring , , Thus, the time-domain continuous dynamic trajectory of DHN is obtained.

[0062] (2) NGN Modeling and Solution (2.1) PDAE model of NGN The transmission of gas within a pipeline is driven by the pressure difference between its two ends, and its spatiotemporal evolution can be characterized by one-dimensional mass and momentum conservation equations. Following common treatments, under the assumptions of isothermal conditions, horizontal installation, and neglect of convective acceleration, the dynamic process of the pipeline can be expressed as the following set of governing equations, with mass conservation constraints applied at the nodes.

[0063] (2.1.1) Equations for Conservation of Mass and Momentum in Pipelines

[0064] (15) In the formula: and Pipes Pressure and mass flow rate; These are the spatial coordinates along the pipeline direction. For time; This refers to the cross-sectional area of ​​the pipe. The speed of sound (can be considered a constant); As the friction factor, This refers to the inner diameter of the pipe. For pressure reciprocal quantity; This is a direction parameter, usually taken as the flow direction sign at the center of the expansion.

[0066] (2.1.2) Nodal mass conservation constraints (16) In the formula: and These are the NGN node set and the pipeline set, respectively. For pipelines In relation to nodes Mass flow rate at the connected port; The node-to-pipeline correlation coefficient; , These refer to the gas supply and gas intake at the nodes, respectively.

[0067] (2.2) NGN Modeling and Solution Based on HEM To facilitate unified solution with nodal mass conservation constraints in time-domain simulation, this embodiment uses each time window Within this framework, pipeline state variables are viewed as "time-embedded variables". "and spatial embedded variables" The partial differential equation is transformed into a recursive linear relationship in the coefficient domain by using a holomorphic embedding expansion. This allows for the successive, stepwise evolution of the pressure and mass flow rate at both ends of the pipeline within a time window.

[0068] (2.2.1) Spatiotemporal two-dimensional holomorphic embedding expansion In the time window Inside, introduce

[0069] (17) And a spatiotemporal two-dimensional holomorphic embedding expansion is performed on pressure, flow rate, and reciprocal:

[0071]

[0072] (18) In the formula: Expand the center for the current time window; This refers to the length of the pipe. To truncate the total order; , , The two-dimensional coefficients of pressure, flow rate, and reciprocal in the coefficient domain (satisfying) ).

[0074] (2.2.2) Rules for operation of coefficient field For any expansion quantity Its partial derivatives satisfy the following in the coefficient domain:

[0075] (19) like Then the product term corresponds to a two-dimensional Cauchy convolution in the coefficient domain: (20) In the formula: for Two-dimensional coefficients; For product Two-dimensional coefficients.

[0077] (2.2.3) Recursive form of the coefficient field of the pipeline equation Substitute equation (18) into equation (15), and use Balancing terms of the same power yields a recursive linear relationship between pressure and flow coefficient: (twenty one) (twenty two) In the formula: For time-order and spatial-order indexes (satisfying) ); The product of three terms The two-dimensional convolution coefficients; Maintain a constant value within a single time window.

[0078] (2.2.4) Reciprocal quantity coefficient recursion To find the coefficient of the reciprocal, we use the identity. (This holds true consistently within the time window), and by balancing the coefficients of the same power, we can obtain... The recurrence relation. From the initial coefficients... Departure, and for any Then the remaining reciprocal coefficients can be calculated step by step.

[0079]

[0080] (twenty three) In the formula: Exclusion when summing Item (i.e., put) (Move to the left side separately); recursion starts from known initial coefficients. and Once you start, you can obtain the remaining reciprocal coefficients step by step.

[0082] (3) EPS modeling and solution (3.1) EPS polar coordinate power flow equation In the electrical thermal time-domain simulation, EPS is treated as steady state: for each time... Solving the first-order steady-state AC power flow algebraic equation yields the bus voltage magnitude and phase angle. In polar coordinates, the active / reactive power injection equations at the nodes can be written as follows:

[0083]

[0084] (twenty four) In the formula: , Inject vectors for active and reactive power of each bus; , This represents the voltage amplitude and phase angle vector. Here is the nodal admittance matrix. , These are the conductivity and susceptance matrices, respectively. , These are the cosine and sine matrices constructed from the phase angle difference; This represents a diagonal matrix constructed from vectors.

[0086] (3.2) EPS Modeling and Solution Based on HEM In the time window Internal Order Expressing voltage amplitude and phase angle as relative to Finite power series:

[0087] (25) And node injection is represented as

[0089] (26) (3.2.1) Recursive derivation of the cosine / sine coefficients of the phase angle difference Define angle difference

[0091] (27)

[0093] (28) Depend on , The coefficient recursion can be obtained ( ):

[0095] (29)

[0097] (30) In the formula: The first angle difference Order coefficient; , They are respectively , The Order coefficient.

[0099] (3.2.2) Nodal active / reactive coefficient equations Substitute equations (25)-(30) into steady-state power flow equation (24), and follow the formulas. Balancing coefficients of the same power yields the result for any : (31) (32) In the formula: For voltage amplitude Order coefficient; For the phase angle Order coefficient; , The coefficients of the cosine / sine matrix are obtained recursively from equations (29) and (30); , The active and reactive power injections of the nodes are respectively the first... The order coefficient. In equations (29)-(32), the first... The order only contains and ,and , right The dependency of appears in linear form through equation (32), therefore, given the bus type constraint, the first can be denoted as . Unknown coefficients of order The system of linear equations of a fixed size is solved step by step.

[0100] In the cross-carrier dynamic simulation of the integrated electrical and thermal energy system, the time scale of EPS is significantly faster than that of NGN / DHN. To reconcile the time scale mismatch, traditional discretization methods often use linear interpolation to align the discrete boundary quantities of DHN to a finer time grid. In contrast, the continuous function obtained by the proposed HEM within the time window can be directly evaluated or its coefficients mapped to complete the coupling at any fine time point, thereby reducing the dependence on additional interpolation alignment and maintaining the temporal continuity of the interface quantities.

[0101] Specifically, the coupling interface expression: The coupling mode of heat-determined electricity / gas is adopted: at the combined heat and power (CHP) unit, the heat power injected into the DHN is first determined by the state of the DHN side. EPS injection is then obtained through a fixed conversion relationship. Equivalent load of NGN Therefore, no outer-layer iteration is required during the coupled advancement process.

[0102] (33) In the formula: For the thermal power injection from CHP to DHN; It is a specific heat at constant pressure; Mass flow rate on the DHN side; , These are the supply and return water temperatures, respectively.

[0103]

[0104] (34) In the formula: Thermoelectric ratio; This is the active power injection from CHP to EPS; This refers to the gas-side conversion efficiency (or equivalent conversion coefficient). This represents the equivalent load of CHP on the NGN side.

[0106] From equations (33) and (34), DHN is given. Then it can be determined and It serves as an external input to EPS and NGN, advancing at their respective time steps.

[0107] Specifically, the continuous function interface is aligned with the coefficient mapping: To accommodate multiple time steps, this embodiment uses truncated power series representations for interface quantities within a time window. , , Taking the number of interfaces as an example, the center is expanded within a certain time window. Nearby is uniformly written as (35) In the formula: Expand the center for the current time window; for exist place Order coefficient; The truncation order in the time domain.

[0108] When EPS / NGN uses a smaller step size, the center of its next solution window is At that time, it is necessary to apply formula (35) to the new center. The area is reopened as (36) In the formula: Set as the center of the next solver window for EPS / NGN; for exist place Order coefficient.

[0109] Using power series translation, we can directly obtain the result from the known... calculate : (37) In the formula: The coefficients are binomial coefficients.

[0110] Equation (37) shows that interface quantities can be aligned through series coefficient mapping between time windows with different step lengths. In this way, EPS / NGN can directly obtain the input coefficients required for solving the window within its fine step length window (or equivalently evaluate them at any fine time point), thereby avoiding the additional error source of "discrete sampling point - interpolation alignment" and maintaining the temporal continuity of interface quantities.

[0111] Specifically, the multi-time-step advancement process: In a unidirectional coupling scenario, multi-time-step coupling propagation can be summarized as follows: DHN coarse step size propulsion: in the first DHN time window Solve for DHN within the window and obtain the result from equation (33). Continuous representation of .

[0112] Interface quantity generation: generated by equation (34) Mapped to and This forms a continuous interface input for EPS / NGN within the DHN time window.

[0113] EPS / NGN fine step size advancement: fine step size time window center for each EPS / NGN The interface quantity coefficients are mapped to according to equation (37). The corresponding expansion form is used as input to drive the recursive solution of HEM in the EPS time domain and HEM in NGN, respectively.

[0114] Time window scrolling: completion interval After advancing all the fine step sizes, proceed to the next DHN time window until the entire simulation time domain is covered.

[0115] The above process is completed in one pass within each DHN time window, and the continuous dynamic response in the time domain of EPS / NGN / DHN can be obtained without outer iteration.

[0116] In this implementation, the simulation configuration and comparison method are given, followed by a comparison of key indicators and result analysis. The effectiveness and accuracy of HEM in the dynamic simulation of integrated electrical and thermal energy systems are evaluated through comparative examples.

[0117] Simulation settings: 1) Comparison Method: To conduct benchmark comparisons, the implicit finite difference method was selected as the discretization comparison method, and its simulation results with subdivided spatial segments were used as the benchmark. Under the same operating conditions and boundary disturbances, simulations were performed using FDM with different spatial segmentation scales to reflect the impact of changes in spatial discretization scale on accuracy and numerical fluctuations. Simultaneously, in the gas / thermal fluid network, the HEM was used for expression and recursive solution in the spatiotemporal two-dimensional domain, and coupled with the time-domain HEM model of EPS to obtain the dynamic response of the integrated electrical and thermal energy system. Finally, the results were aligned and compared with the benchmark results.

[0118] 2) Key indicators: Two indicators are selected for accuracy assessment: mean absolute error (MAE) and mean absolute percentage error (MAPE).

[0119] 3) Simulation environment: All simulations were performed on the MATLAB R2025a platform, and the hardware was a laptop equipped with an AMD Ryzen 7 5800H processor (3.20GHz) and 16GB of memory.

[0120] EGH-IES-1 calculation example: 1) Case settings The proposed time-domain continuous HEM coupled simulation framework is evaluated using the example EGH-IES-1. The system consists of a 14-node EPS, a 13-node NGN, and a 54-node DHN, which are coupled energyly through a CHP device: the CHP draws gas from the NGN and injects electrical power into the EPS and thermal power into the DHN; the system structure and topology are as follows. Figure 2 As shown.

[0121] 2) Boundary settings The simulation time domain length was set to 3600s. To reflect the time scale differences of each subsystem, EPS and NGN used a 1s step size, while DHN used a 10s step size. In the baseline FDM, time step mismatch was addressed by aligning the discrete boundary quantities of DHN to a finer time grid through linear interpolation to achieve coupling. However, in the proposed continuous coupling simulation strategy in the time domain, the continuous function / series reconstruction obtained by HEM within the time window allows for direct evaluation at any time point to complete coupling, thus avoiding dependence on additional interpolation alignment. To verify the dynamic tracking capability of the method under disturbance conditions, this embodiment uniformly applied random step disturbances to the electrical and thermal boundary quantities. Specifically, coefficient disturbances were applied to the electrical load, gas load, and thermal load: the disturbance coefficients were randomly generated within the interval [0.8, 1.2] and updated in a step manner, with the thermal load updated every 600s and the gas and electrical loads updated every 200s, thus forming a random disturbance sequence with multiple steps across the entire time domain, used to examine the response accuracy and numerical stability of different solution methods to abrupt boundary changes.

[0122] 3) Comparison Objects Benchmark: DHN uses a spatial step size of Using FDM as a benchmark, NGN adopts a spatial step size of The FDM is used as the benchmark.

[0123] FDM Control Group: To demonstrate the impact of spatial segmentation scale variations on accuracy and numerical fluctuations, four groups of spatially segmented FDM were set up as controls, namely... , ; , ; , ; , .

[0124] In this embodiment, the HEM proposed is as follows: the NGN / DHN subsystem constructs a spatiotemporal two-dimensional HEM expression within the pipe segment, while the EPS subsystem adopts a time-domain HEM model; the spatial step size is adopted. and .

[0125] 4) Simulation Results like Figures 3-8As shown, when frequent step disturbances exist at the electrical-thermal boundary, the slowly varying response of DHN, the propagating response of NGN, and the fast response of EPS are highly consistent with the fine-mesh FDM baseline curve, thus accurately characterizing the cross-network energy interaction process. Furthermore, under multiple time-step conditions—EPS and NGN with a step size of 1s and DHN with a step size of 10s—HEM achieves cross-timescale information transfer through a continuous function / series interface. This allows the coupled simulation to maintain continuous output in the time domain while reducing its dependence on additional interpolation alignment, thus better meeting the needs of multi-network joint online analysis.

[0126] Tables 1 and 2 show the MAE / MAPE and computation time for each method. The results show that as the space step size of FDM gradually increases from the baseline, the total simulation time decreases, but the MAE / MAPE of key quantities such as return water temperature, CHP thermal output, mass flow rate, and pressure increase, reflecting a typical trade-off between accuracy and efficiency. In contrast, HEM achieves significant acceleration while maintaining high accuracy: taking Table 1 as an example, the total simulation time of HEM decreased from 7512.406s for the baseline FDM to 358.754s, an acceleration of approximately 21 times; simultaneously, its return water temperature error is only... , The CHP thermal output error is , The error level is significantly better than that of coarse-segmented FDM (other indicators are shown in Table 2). For NGN and EPS, HEM also maintains a very small error magnitude (e.g., voltage amplitude / phase angle error reaches 100%). The magnitude indicates that the method has a stable high-fidelity output capability under cross-network coupling conditions.

[0127] Table 1. Simulation Return Water Temperature and CHP Thermal Output Parameters and Total Simulation Time for EGH-IES-1

[0128] Table 2 EGH-IES-1 Simulated NGN and EPS Indicators

[0129] comprehensive Figures 3-8 As shown in Tables 1-2, HEM can maintain a time-domain response consistent with the FDM benchmark under multiple step disturbances, and exhibits better accuracy-efficiency performance in the scenario of "multi-time-step coupling + continuous time-domain output", providing an efficient implementation path for continuous dynamic simulation of electrical and thermal integrated energy systems in the time domain.

[0130] This embodiment addresses the dynamic simulation requirements of integrated electrical and thermal energy systems by constructing a time-domain continuous coupling simulation strategy based on the HEM model. A spatiotemporal HEM model is proposed within the gas / thermal fluid network to characterize the transport process described by the PDE, and it is consistently coupled with the EPS polar coordinate form of the HEM model and the steady-state relationships of the coupled devices. Simultaneously, considering the cross-timescale characteristics of the coexistence of fast dynamics in EPS and slow dynamics in gas / thermal systems, a multi-time-step time-domain continuous coupling strategy is proposed. Asynchronous information transmission is achieved through a continuous function / series interface, fundamentally reducing interpolation dependencies and maintaining continuous output. The results show that, using a fine-mesh FDM as a benchmark, at the same spatial step size (DHN5m, NGN100m), HEM reduces the simulation time from 7512.406s to 358.754s (approximately 20.9× acceleration), while maintaining high accuracy in key indicators—return water temperature. , CHP heat output , Regarding NGN and EPS metrics, mass flow rate , ,pressure , Voltage amplitude , Voltage phase angle , .

[0131] The above results demonstrate that the proposed method can significantly improve computational efficiency while ensuring high accuracy, and provides simulation results of continuous time-domain trajectories to support the operation verification and control evaluation of integrated electrical and thermal energy systems.

[0132] Example 2 This embodiment discloses a modeling and simulation system for a fully embedded integrated electrical and thermal energy system, including: The electrical thermal model building module is configured to: build a dynamic model of a heating network based on full embedding, a dynamic model of a natural gas network based on full embedding, and a dynamic model of a power system based on full embedding. The coupling interface module is configured to adopt a heat-determined electricity / gas coupling mode, determine the amount of interface injected into the heating network based on the status of the heating network side, and then obtain the amount of interface injected into the power system and the amount of interface injected into the natural gas network through a fixed conversion relationship. The multi-time-step strategy configuration module is configured to: advance the simulation strategy with a multi-time-step approach: advance the solution of the heating network dynamic model with a coarse step size, obtain the continuous representation of the interface quantity within a certain time window, and then map it to the interface quantity of the power system and the natural gas network, forming a continuous interface input of the power system and the natural gas network within the time window; and advance the solution of the power system dynamic model and the natural gas network dynamic model with a fine step size. The dynamic response module is configured to: based on the advancement of the multi-time-step simulation strategy, recursively solve the coefficients of each order of the dynamic model of the heating network, the dynamic model of the natural gas network, and the dynamic model of the power system, to obtain the continuous dynamic response of the integrated electrical and thermal energy system in the simulation time domain.

[0133] Example 3 The purpose of this embodiment is to provide a computer-readable storage medium.

[0134] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the modeling and simulation method for a fully embedded integrated electrical and thermal energy system as described in Embodiment 1 of this disclosure.

[0135] Example 4 The purpose of this embodiment is to provide an electronic device.

[0136] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the modeling and simulation method for a fully embedded integrated electrical and thermal energy system as described in Embodiment 1 of this disclosure.

[0137] The steps and methods involved in the apparatuses of Embodiments 2, 3, and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0138] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0139] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A modeling and simulation method for a fully embedded integrated electrical-thermal energy system, characterized in that, include: Dynamic models of heating networks, natural gas networks, and power systems based on fully embedded systems were constructed respectively. The coupling mode of heat-determined electricity / gas is adopted. The interface quantity injected into the heating network is determined by the state of the heating network side, and the interface quantity injected into the power system and the interface quantity of the natural gas network are obtained by a fixed conversion relationship. The simulation strategy employs multiple time steps: the dynamic model of the heating network is solved under a coarse step size, and the continuous representation of the interface quantities within a certain time window is obtained and mapped to the interface quantities of the power system and the natural gas network, forming continuous function / series interface inputs of the power system and the natural gas network within that time window; the dynamic model of the power system and the dynamic model of the natural gas network are solved under a fine step size. Based on the advancement of the multi-time-step simulation strategy, the coefficients of each order of the dynamic model of the heating network, the dynamic model of the natural gas network, and the dynamic model of the power system are solved recursively to obtain the continuous dynamic response of the integrated electrical and thermal energy system in the simulation time domain.

2. The modeling and simulation method for a fully embedded integrated electrical and thermal energy system as described in claim 1, characterized in that, The construction of the dynamic model of the heating network based on fully embedded systems includes: Within the time window, two-dimensional spatiotemporal holomorphic coefficients of mass flow rate, pressure, and water temperature in the heating pipeline are defined and reconstructed into a spatiotemporal continuous expression. Substituting the spatiotemporal continuous expression into the hydraulic-thermal dynamic equation of the pipeline and matching the coefficients of the same order, a set of recursive linear equations is obtained. In the recursive forms of the momentum equation and the energy equation, the higher-order coefficients are obtained only by linear calculation of the lower-order coefficients.

3. The modeling and simulation method for a fully embedded integrated electrical and thermal energy system as described in claim 2, characterized in that, The construction of the dynamic model of the heating network based on fully embedded systems also includes: For heating network nodes, the node mass conservation, energy conservation, and temperature mixed constraints are expanded into power series in the time domain, substituted into the node algebraic equations, and the coefficient recursive relationship of the node model is established. Among them, the conservation of nodal mass and energy are given linear constraints at each time order; For the fractional nonlinearity in the nodal temperature mixing equation, a recursive method of finding the inverse of holomorphic functions is adopted. By constructing the holomorphic inverse function of the denominator, the division operation is transformed into a convolution operation, and the power series coefficients of the nodal temperature are obtained.

4. The modeling and simulation method for a fully embedded integrated electrical and thermal energy system as described in claim 1, characterized in that, The construction of the dynamic model of the natural gas network based on fully embedded systems includes: Within a time window, the pressure, mass flow rate, and reciprocal of pressure of the natural gas pipeline are defined as two-dimensional spatiotemporal holomorphic coefficients in the spatiotemporal domain and reconstructed into a spatiotemporal continuous expression. Substituting the spatiotemporal continuous expression into the partial differential equations for mass and momentum conservation of the pipeline, and using the coefficient domain partial derivative rule and convolution rule, the coefficients of terms of the same power are matched to obtain the coefficient recursive relationship of the natural gas pipeline model. By utilizing the relationship that the product of pressure and its reciprocal is always equal to 1, the recursive relationship of the pressure reciprocal coefficient is obtained by balancing the coefficients of the same power.

5. The modeling and simulation method for a fully embedded integrated electrical and thermal energy system as described in claim 1, characterized in that, The construction of a power system dynamic model based on fully embedded systems includes: Within the time window, the voltage magnitude and phase angle of the bus are expressed as power series with respect to the time-embedded variable, and the active and reactive power injected into the nodes are also expressed as power series. Define the phase angle difference and recursively obtain the power series coefficients of the cosine and sine functions of the phase angle difference; Substituting the power series coefficients into the polar coordinate form of the nodal active / reactive power injection equations and matching the coefficients of the same power, we obtain the coefficient recursive linear equation system of the power system model.

6. The modeling and simulation method for a fully embedded integrated electrical and thermal energy system as described in claim 1, characterized in that, The interface quantities are the thermal power injected into the heating network, the electrical power injected into the power system, and the equivalent load of the natural gas network.

7. The modeling and simulation method for a fully embedded integrated electrical and thermal energy system as described in claim 1, characterized in that, The mapping is the interface quantity between the power system and the natural gas network, including: the power series coefficients of the interface quantity at the center of the coarse-step long time window are obtained by power series translation to obtain the power series coefficients of the interface quantity at the center of the fine-step long time window, and the input coefficients required for solving the fine-step long time window are directly obtained.

8. A modeling and simulation system for a fully embedded integrated electrical and thermal energy system, characterized in that, include: The electrical thermal model building module is configured to: build a dynamic model of a heating network based on full embedding, a dynamic model of a natural gas network based on full embedding, and a dynamic model of a power system based on full embedding. The coupling interface module is configured to adopt a heat-determined electricity / gas coupling mode, determine the amount of interface injected into the heating network based on the status of the heating network side, and then obtain the amount of interface injected into the power system and the amount of interface injected into the natural gas network through a fixed conversion relationship. The multi-time-step strategy configuration module is configured to: advance the simulation strategy with a multi-time-step approach: advance the solution of the heating network dynamic model with a coarse step size, obtain the continuous representation of the interface quantity within a certain time window, and then map it to the interface quantity of the power system and the natural gas network, forming the continuous function / series interface input of the power system and the natural gas network within the time window; and advance the solution of the power system dynamic model and the natural gas network dynamic model with a fine step size. The dynamic response module is configured to: based on the advancement of the multi-time-step simulation strategy, recursively solve the coefficients of each order of the dynamic model of the heating network, the dynamic model of the natural gas network, and the dynamic model of the power system, to obtain the continuous dynamic response of the integrated electrical and thermal energy system in the simulation time domain.

9. A computer-readable storage medium having a program stored thereon, characterized in that, When executed by the processor, the program implements the steps in the modeling and simulation method for a fully embedded electrical-thermal integrated energy system as described in any one of claims 1-7.

10. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the modeling and simulation method for a fully embedded electrical-thermal integrated energy system as described in any one of claims 1-7.

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