Quantitative state projection integral simulation method for multi-energy system containing electric hydrogen coupling fast charging station

Abstract

The application discloses a multi-energy system quantitative state projection integral simulation method containing an electric hydrogen coupling fast charging station, belongs to the technical field of multi-energy system dynamic simulation and numerical integral, and comprises the following steps: establishing an overall dynamic simulation model of simultaneous power grid power flow, gas network pipeline transmission, fast charging station and fuel cell model; in the inner layer integral time, the integral step is calculated based on the third derivative of the system state variable, and the state discrete event and power grid power flow updating event are detected to accurately locate the event time; when the inner layer integral times reach the preset value, the outer layer performs large step projection extrapolation based on the recent state change trend, and the projection result is checked for events; through the alternating execution of the inner layer fine integral and the outer layer projection, the dynamic simulation of the multi-energy system containing the electric hydrogen coupling fast charging station is realized. The application effectively integrates the quantitative state system and the projection integral algorithm by using the above method, and improves the calculation efficiency of the dynamic simulation of the multi-energy system containing the electric hydrogen coupling fast charging station.

Description

Technical Field

[0001] This invention relates to the field of dynamic simulation and quantized state projection integration technology for multi-energy systems, and in particular to a quantized state projection integration simulation method for multi-energy systems including electric-hydrogen coupled fast charging stations. Background Technology

[0002] Driven by the "dual carbon" goals, both the electric vehicle industry and renewable energy have experienced explosive growth. The rapid development of super-fast charging technology has increased the single-gun charging power from the early 60kW to 350kW and even over 480kW, significantly shortening the charging time for electric vehicles. However, the instantaneous high-power load brought by super-fast charging can severely impact the power distribution network. To address this, the hydrogen-electric coupling fast charging station has emerged. It integrates a super-fast charging pile and a hydrogen fuel cell, using the hydrogen fuel cell to power the system and mitigate the drastic fluctuations caused by the super-fast charging load, thus achieving coupled operation of the power grid, hydrogen grid, and electric vehicle fast charging station.

[0003] Dynamic simulation of multi-energy systems including fast charging stations with hydrogen-electric coupling faces two main technical challenges: First, the time scale of hydrogen propagation ranges from minutes to hours, while the time scale of electric vehicle fast charging ranges from seconds to minutes. The time constants of different subsystems differ significantly, resulting in a typical rigidity characteristic of the simulation system. Second, a series of discrete state events are triggered during the simulation, such as adjustments to fuel cell operating strategies and the opening and closing of gas network pressure valves. The timing of these events needs to be precisely located; otherwise, the simulation accuracy will decrease.

[0004] For rigid systems, traditional explicit numerical integration methods require extremely small step sizes due to stability constraints, resulting in low computational efficiency. Traditional implicit methods, on the other hand, involve numerous matrix operations and solving nonlinear equations for large-scale problems, placing a heavy computational burden on them. Projective integration algorithms, by combining inner-layer small-step integration with outer-layer large-step extrapolation, alleviate the efficiency bottleneck caused by rigidity problems to some extent. Quantized state system methods, by discretizing state variables into quantized intervals, trigger computation only when state changes exceed quantum values, possessing the ability to explicitly locate discrete event moments. However, current technologies have not yet effectively integrated these two approaches, and when simultaneously dealing with multi-timescale rigidity and frequent discrete events, it remains difficult to balance simulation efficiency and accuracy. Summary of the Invention

[0005] The purpose of this invention is to provide a quantitative state projection integral simulation method for multi-energy systems containing electric hydrogen coupling fast charging stations, in order to solve the problem that existing simulation technologies are unable to simultaneously cope with rigid and frequent discrete events at multiple time scales, resulting in low computational efficiency and slow simulation speed, and to achieve efficient and accurate dynamic simulation of multi-energy systems containing electric hydrogen coupling fast charging stations.

[0006] To achieve the above objectives, this invention provides a quantitative state projection integral simulation method for a multi-energy system including an electro-hydrogen coupling fast charging station, comprising the following steps: S1. Simulation Initialization: Based on the selected multi-energy system including the electric-hydrogen coupling fast charging station, determine the grid parameters, hydrogen network parameters, electric vehicle fast charging station parameters, fuel cell parameters, and simulation control parameters; the simulation control parameters include the inner layer integral number. and outer projection number ;Inner layer integrator counter Set to zero; S2. Establish a system-wide dynamic simulation model: Establish a dynamic simulation model of the multi-energy system, including a power grid flow model, a gas pipeline transmission model, an electric vehicle fast charging station model, and a fuel cell model; combine the above models to form a system-wide dynamic simulation model of the multi-energy system, which includes a system of differential equations and a system of algebraic equations; define the system state variables. and system control variables The system differential equations are used to describe the system state variables. Relationship changing over time; S3. Determine the current state of the inner layer integrator counter: Determine the current state of the inner layer integrator counter. Does the value reach the inner integral number? If the target is reached, proceed to step S7; otherwise, proceed to step S4. S4. Calculate the derivative and preliminary integration step size: Based on the overall dynamic simulation model, calculate the derivative and preliminary integration step size at the current simulation time. Below, system state variables first derivative Second derivative and third derivative And based on the third derivative, a preliminary inner-layer integration step size is calculated. ; S5. Determine the target inner-layer integration step size: Determine the multi-energy system's time interval. Does the internal state discrete event or power flow update event trigger? If any event is triggered, the initial inner integration step size should be adjusted according to the time of the event. The corrected step size is then determined as the target inner-layer integration step size. ; If no event is triggered, the initial inner integration step size will be... Directly determined as the inner integration step size of the target .

[0007] S6. Perform inner integration: Use the target inner integration step size. and first derivative Second derivative and third derivative Based on the overall dynamic simulation model, the multi-energy system is calculated at time t. System state variables and update the system state variables; set the inner integral counter. The value is increased by one; the simulation time is defined as follows after the update. The updated simulation time is used as the new current simulation time. This will be used as a reference for subsequent steps; then proceed to step S9.

[0008] S7. Perform outer projection: Based on the system state variables at the current simulation time... value and at the moment value The number of projections is the number of outer projections. Extrapolation calculations are performed to obtain the outer layer projection result; the inner layer integrator counter is then used. Set to zero.

[0009] S8. Verify the validity of the outer projection: Determine the validity of the multi-energy system within the time interval. Does the internal state discrete event or power flow update event trigger? If any event is triggered, return to step S4; If no event is triggered, accept the outer projection result and use the outer projection result as the time of the multi-energy system. The system state variables are used to update the system state variables in the overall dynamic simulation model; the updated simulation time is defined as... The updated simulation time is then used as the new current simulation time. For reference in subsequent steps; then proceed to step S9; S9. Determine the simulation termination condition: Determine the current simulation time. Has the preset simulation end time been reached? If it has, terminate the simulation; otherwise, return to step S3.

[0010] Preferably, in step S1: Power grid parameters include network topology, branch resistance, and branch reactance; Hydrogen network parameters include pipe length, pipe diameter, pipe friction coefficient, pipe angle with the horizontal direction, sound velocity in hydrogen, compressor operating parameters, and pipe micro-segment length. The parameters for electric vehicle fast charging stations include road traffic flow, charging pile charging power, nodal electricity price, and charging vehicle battery level. Fuel cell parameters include battery operating temperature, maximum battery current density, proton exchange membrane internal resistance, proton membrane thickness, battery area, number of cells in series, anode capacity, anode channel outlet orifice coefficient, and supply pipe outlet orifice coefficient. The simulation control parameters also include simulation start time, simulation end time, and quantum value.

[0011] Preferably, in step S2, the overall dynamic simulation model is composed of the following models: S21. Power Flow Model: Ignoring transient processes in the power grid, an AC power flow calculation model is adopted. S22. Gas Pipeline Transport Model: The hydrogen pipeline space is discretized into several pipeline micro-elements. For each pipeline micro-element, the partial differential equation describing gas transport is transformed into an ordinary differential equation using the method of characteristics. The transport equation for a small element of a pipe segment is: ; ; In the formula, For the first The gas pressure of a micro-element in a section of the pipeline. For the first Gas flow rate of a micro-element in a pipeline segment The speed of sound in hydrogen gas. The cross-sectional area of ​​the pipe. This is the pipe friction coefficient. For pipe diameter, It is the acceleration due to gravity. The angle between the pipe and the horizontal direction. and Let be the difference functions along the positive and negative characteristic lines, respectively, defined as: ; ; In the formula, Let the length of the pipe element be denoted as . For the spatial coordinate variables along the pipeline, For the first Spatial coordinates of the center point of the micro-element of the pipeline segment. These are general physical quantity symbols used when calculating pressure equations. Specifically refers to When calculating the flow equation, Specifically refers to ; and The first Section and the General physical quantities on a micro-element of a pipe segment For time; S23. Electric Vehicle Fast Charging Station Model: The differential equation for the electric vehicle charging process is: ; In the formula, The charging power of the fast charging station The state of charge (SOC) of an electric vehicle; The number of vehicles charging is determined by the current traffic flow and charging threshold. The current battery level of vehicles on the road section follows a normal distribution, and vehicles with a battery level below the charging threshold enter the fast charging station for charging. Each fast charging station connects to a distribution network node that uses dynamic electricity pricing. The non-linear electricity pricing function relationship between the node voltage and the charging price is as follows: ; In the formula, For nodes The charging price, For nodes voltage, , The coefficients of the electricity price function are denoted as .

[0012] The piecewise linear relationship between user charging threshold and nodal electricity price is as follows: ; In the formula, For nodes The charging threshold, This is the upper limit of the charging threshold. This is the lower limit of the charging threshold. , Electricity price parameters; S24. Fuel cell model: including voltage power model and hydrogen reaction flow channel model; In the voltage-power model, the fuel cell stack consists of It is composed of identical single cells connected in series, and the voltage of a single cell is... for: ; fuel cell voltage for: ; fuel cell output power for: ; Fuel cell net output power for: ; In the formula, This is the battery's thermodynamic potential. To activate the polarization overpotential, For concentration polarization overpotential, For Ohm overpotential, For fuel cell current, The power consumed by the air compressor that supplies oxygen to the cathode; The differential equation for the hydrogen reaction flow channel model is: ; In the formula, Here is the molar mass of hydrogen. For anode capacity, The gas constant is Battery operating temperature This refers to the hydrogen gas pressure at the anode of the fuel cell. , , These represent the anode inlet, outlet, and consumed hydrogen mass flow rates, respectively. S25. By combining the power grid flow model, gas pipeline transmission model, electric vehicle fast charging station model, and fuel cell model, the standard form of the overall dynamic simulation model is obtained: ; In the formula, For system state variables, For system control variables, The system consists of a set of differential equations. For the system of algebraic equations, System state variables The first derivative with respect to time, i.e. .

[0013] Preferably, in step S4, the first derivative Second derivative and third derivative The calculation formula is: ; ; ; In the formula, For system control variables, For the system control variables at the current simulation time The value, The system consists of a set of differential equations. , These are the first and second derivative expressions of the system's differential equations, respectively.

[0014] Preferably, in step S4, the initial inner layer integration step size Calculate using the following formula: ; In the formula, For the quantum value of the state variable, For the system state variables at the current simulation time The third derivative. This formula means: calculate the candidate step size for each state variable, and take the minimum value as the initial inner integration step size. .

[0015] Preferably, step S5 includes the following sub-steps: S51. Determine if a state discrete event has been triggered: No. The boundary of the discrete event for each state variable is: ,exist The criterion for discrete events in an internally triggered state is: ; In the formula, For the current simulation moment The next The values ​​that a state variable can take. To integrate according to the initial inner layer step size The estimated value after implementation; If a discrete state event is triggered, the step size that satisfies the following equation is calculated. : ; and with As the inner integration step size of the target; In the formula, These are the current simulation times. Next The first, second, and third derivatives of each state variable; S52. Determine if a power flow update has been triggered: For the next power grid flow update time, if The system determines that a power flow update is triggered within the time interval and adjusts the initial inner-layer integration step size accordingly. The corrected step size is used as the target inner layer integration step size; S53. If neither the state discrete event nor the power grid flow update is triggered, then the initial inner-layer integration step size will be adjusted. Directly determined as the inner integration step size of the target .

[0016] Preferably, in step S6, the multi-energy system at time... System state variables Calculate using the following formula: .

[0017] Preferably, in step S7, the outer projection result is calculated using the following formula: ; In the formula, This is the result of the outer projection.

[0018] Preferably, step S8 includes the following sub-steps: S81. Determine if a state discrete event has been triggered: No. The boundary of the discrete event for each state variable is: ,exist The criterion for discrete events in an internally triggered state is: ; In the formula, For the current simulation moment Next The values ​​that a state variable can take. To be based on the outer projection step size The estimated value after implementation; S82. Determine if a power flow update has been triggered: For the next power grid flow update time, if The system determines that a power flow update is triggered within the time interval. S83. If any event in step S81 or step S82 is triggered, return to step S4. S84. If neither the state discrete event nor the power grid flow update is triggered, then accept the outer projection result and update the system state variables according to the following formula: ; In the formula, This is the outer projection result obtained in step S7.

[0019] Therefore, the present invention employs the above-mentioned quantized state projection integral simulation method for multi-energy systems containing electro-hydrogen coupling fast charging stations, which has the following beneficial effects: (1) High simulation efficiency. This invention adopts a two-layer time stepping strategy that combines inner-layer fine integration with outer-layer projection extrapolation. When the system changes smoothly, large-step projection replaces a large number of small-step integrations, significantly reducing the number of calculations. The simulation time is reduced to about 1 / 2.75 of that of RKF45 and about 37.5% of that of EPIM.

[0020] (2) Adaptive step size adjustment. This invention automatically adjusts the inner integration step size based on the third derivative and quantum value of the system state variables. When the changes are drastic, the step size is reduced to ensure accuracy, and when the changes are gradual, the step size is increased to save computation. This avoids the problem that the efficiency and accuracy of the traditional fixed step size method are difficult to balance.

[0021] (3) Accurate event location. The present invention sets up detection and step size correction mechanisms for discrete state events and power grid power flow updates in both the inner and outer layers, which can accurately locate the event triggering time and avoid simulation distortion caused by large step size of the outer layer projection spanning multiple events.

[0022] (4) Comprehensive system modeling. This invention integrates four sub-models: power grid, gas grid, fast charging station and fuel cell, and introduces dynamic electricity price and user charging behavior decision model, realizing closed-loop coupled simulation of physical system and economic behavior, and the simulation results are closer to the actual operating conditions.

[0023] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0024] Figure 1 This is a flowchart of the quantitative state projection integral simulation method for a multi-energy system including an electro-hydrogen coupling fast charging station, as described in this invention. Figure 2 It is a 20-node gas network topology; Figure 3 It is the IEEE 33-node power grid topology; Figure 4 This is a graph showing the pressure change over time at node 12 of the gas network in an example of the present invention. Figure 5 This is a graph showing the voltage variation over time at grid node 21 in an example of the present invention. Figure 6 This is a graph showing the relative pressure error of gas network node 12 over time in an example of the present invention. Figure 7 This is a graph showing the change of the relative voltage error of grid node 21 over time in an example of the present invention. Detailed Implementation

[0025] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0026] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0027] Example 1 like Figure 1 As shown, the quantitative state projection integral simulation method for a multi-energy system including an electro-hydrogen coupling fast charging station includes the following steps: S1. Simulation Initialization: Based on the selected multi-energy system including the electric-hydrogen coupling fast charging station, determine the grid parameters, hydrogen network parameters, electric vehicle fast charging station parameters, fuel cell parameters, and simulation control parameters; the simulation control parameters include the inner layer integral number. and outer projection number ;Inner layer integrator counter Set to zero; The parameters for the power grid include network topology, branch resistance, and branch reactance; the parameters for the hydrogen network include pipe length, pipe diameter, pipe friction coefficient, pipe angle with the horizontal direction, speed of sound in hydrogen, compressor operating parameters, and pipe micro-segment length; the parameters for the electric vehicle fast charging station include road flow rate, charging pile charging power, node electricity price, and charging vehicle power; the parameters for the fuel cell include battery operating temperature, maximum battery current density, proton exchange membrane internal resistance, proton membrane thickness, battery area, number of cells in series, anode capacity, anode channel outlet orifice coefficient, and supply pipe outlet orifice coefficient; the simulation control parameters also include simulation start time, simulation end time, and quantum value.

[0028] S2. Establish a system-wide dynamic simulation model: Establish a dynamic simulation model of the multi-energy system, including a power grid flow model, a gas pipeline transmission model, an electric vehicle fast charging station model, and a fuel cell model; combine the above models to form a system-wide dynamic simulation model of the multi-energy system, which includes a system of differential equations and a system of algebraic equations; define the system state variables. and system control variables The system differential equations are used to describe the system state variables. Relationship changing over time; The process of establishing each sub-model is explained in detail below.

[0029] S21. Power Flow Model: Considering that the time scale of power system transient processes is much smaller than that of hydrogen propagation, the transient processes of the power grid are ignored, and the commonly used AC power flow calculation model is adopted. This model consists of a set of algebraic equations used to solve for the voltage magnitude and phase angle of each node based on the injected power.

[0030] S22, Gas Network Pipeline Transmission Model: The hydrogen transport process in a pipeline can be described by the following two partial differential equations, which satisfy the continuity equation and the momentum equation, respectively: ; ; In the formula, This refers to gas pressure. For gas flow rate, The speed of sound in hydrogen gas. The cross-sectional area of ​​the pipe. This is the pipe friction coefficient. For pipe diameter, It is the acceleration due to gravity. The angle between the pipe and the horizontal direction. x These are the spatial coordinates along the pipeline axis; t For time; The pipeline is spatially discretized, and the length of each pipeline element is... For each infinitesimal element of the pipe segment, the method of characteristics is used, and different upwind difference schemes are adopted according to different characteristic line directions to transform the above partial differential equations into ordinary differential equations. The transport equation for a small element of a pipe segment is: ; ; In the formula, For the first The gas pressure of a micro-element in a section of the pipeline. For the first Gas flow rate of a micro-element in a pipeline segment and Let be the difference functions along the positive and negative characteristic lines, respectively, used to approximate the spatial partial derivatives of the physical quantity, defined as: ; ; In the formula, For the first Spatial coordinates of the center point of the micro-element of the pipeline segment. These are general physical quantity symbols used in gas network pipeline transmission equations, when calculating pressure equations. Specifically refers to When calculating the flow equation, Specifically refers to ; and The first Section and the General physical quantities on a segment of pipe micro-element; S23. Electric Vehicle Fast Charging Station Model: The differential equation for the electric vehicle charging process is: ; In the formula, The charging power of the fast charging station This refers to the State of Charge (SOC) of an electric vehicle. The number of vehicles charging is determined by the current traffic flow on the road segment and the charging threshold. Assuming that the current battery level of vehicles on the road segment follows a normal distribution, vehicles with battery levels below the charging threshold need to enter a fast charging station for charging. From this, we can obtain the number of vehicles that need charging and the current battery level of these vehicles.

[0031] Each fast-charging station connects to a distribution network node using a dynamic electricity pricing mechanism. Assuming the current node voltage determines the charging price for the next period, the relationship between node voltage and charging price follows a non-linear electricity pricing function: ; In the formula, For nodes The charging price, For nodes voltage, , The coefficients of the electricity price function are denoted as .

[0032] The piecewise linear relationship between user charging threshold and nodal electricity price is as follows: ; In the formula, For nodes The charging threshold, This is the upper limit of the charging threshold. This is the lower limit of the charging threshold. , Electricity price parameters; This model couples the physical charging process of fast charging stations with the economic decision-making of users' charging behavior, enabling the simulation to reflect the feedback impact of electricity price changes on charging load.

[0033] S24. Fuel cell model: including voltage power model and hydrogen reaction flow channel model; In the voltage-power model, the fuel cell stack consists of It is composed of identical single cells connected in series, and the voltage of a single cell is... It equals the battery thermodynamic potential minus the voltage loss caused by activation polarization, concentration polarization, and ohmic polarization, and is described by the following equation: ; fuel cell voltage for: ; fuel cell output power for: ; Fuel cell net output power for: ; In the formula, This is the battery's thermodynamic potential. To activate the polarization overpotential, For concentration polarization overpotential, For Ohm overpotential, For fuel cell current, The power consumed by the air compressor that supplies oxygen to the cathode; The specific calculation formulas for each potential and overpotential are as follows: ; ; ; ; In the formula, For the Gibbs free energy change, For entropy change, It is Faraday's constant. The gas constant is and The pressure of hydrogen and oxygen. Battery operating temperature For battery standard temperature, These are empirical parameters. Oxygen concentration, This represents the actual current density of the battery. This represents the battery's maximum current density. The coefficients of the equation, The resistivity of the proton membrane to electron flow. The thickness of the proton exchange membrane. This represents the proton membrane area.

[0034] In the hydrogen reaction flow channel model, the change in hydrogen pressure at the anode of the fuel cell is described by the following differential equation: ; The formula for calculating the hydrogen mass flow rate of each part is as follows: ; ; ; In the formula, Here is the molar mass of hydrogen. For anode capacity, The gas constant is Battery operating temperature This refers to the hydrogen gas pressure at the anode of the fuel cell. 、 、 These represent the anode inlet, outlet, and consumed hydrogen mass flow rates, respectively. To supply hydrogen pressure to the pipeline, To supply the outlet orifice coefficient of the pipeline, Set the outlet valve pressure value. Outlet valve coefficient; S25. By combining the power grid flow model, gas pipeline transmission model, electric vehicle fast charging station model, and fuel cell model, the standard form of the overall dynamic simulation model is obtained: ; In the formula, These are system state variables, including the gas pressure of each pipe element. and traffic State of charge of electric vehicles at each fast charging station Fuel cell anode hydrogen pressure wait; These are system control variables, including compressor operating parameters and fast charging station charging power; The system consists of a set of differential equations. The system consists of a set of algebraic equations, including power flow equations and voltage-price relationships. System state variables The first derivative with respect to time, i.e. .

[0035] This standard comprehensively reflects the mutual coupling relationship among four heterogeneous energy subsystems—grid, gas grid, fast charging station, and fuel cell—in a multi-energy system containing an electric-hydrogen coupled fast charging station, and serves as the basis for subsequent dynamic simulation calculations.

[0036] S3. Determine the current state of the inner layer integrator counter: Determine the current state of the inner layer integrator counter. Does the value reach the inner integral number? If the target is reached, proceed to step S7; otherwise, proceed to step S4. S4. Calculate the derivative and preliminary integration step size: Based on the overall dynamic simulation model, calculate the derivative and preliminary integration step size at the current simulation time. Below, system state variables first derivative Second derivative and third derivative And based on the third derivative, a preliminary inner-layer integration step size is calculated. ; First derivative Second derivative and third derivative The calculation formula is: ; ; ; In the formula, For the system control variables at the current simulation time The value, The system consists of a set of differential equations. , These are the first and second derivative expressions of the system's differential equations, respectively.

[0037] Calculate the initial inner-layer integration step size based on the third derivative. The method is as follows: First, calculate the candidate step size based on the third derivative of each state variable, and then select the minimum value as the initial inner integration step size. The calculation formula is: ; In the formula, Let be the quantum value of the state variable. The physical meaning of this formula is: within a given allowable range of change (quantum value) for the state variable, estimate the maximum allowable integration step size based on the third derivative of the current state variable (i.e., the rate of change of acceleration). The more drastic the change (the larger the third derivative), the shorter the step size; the more gradual the change, the longer the step size. This adaptive step size control mechanism based on quantized states is one of the core features that distinguishes this invention from traditional fixed-step-size simulation methods.

[0038] S5. Determine the target inner-layer integration step size: Determine the multi-energy system's time interval. Does the internal state discrete event or power flow update event trigger? Step S5 includes the following sub-steps: S51. Determine if a state discrete event has been triggered: No. The boundary of the discrete event for each state variable is: ,exist The criterion for discrete events in an internally triggered state is: ; In the formula, For the current simulation moment The next The values ​​that a state variable can take. To integrate according to the initial inner layer step size The estimated value after implementation; The meaning of this criterion is: if the state variable is on the opposite side of the event boundary at the current time and the estimated next time, it means that the event boundary must have been crossed within the time interval, that is, the discrete state event has been triggered.

[0039] If a discrete state event is triggered, the step size that satisfies the following equation is calculated. : ; In the formula, These are the current simulation times. Next The first, second, and third derivatives of each state variable are given in the above equation, which is constructed based on a third-order Taylor expansion. A root-finding algorithm is used to precisely solve for the state variables, showing that they exactly reach the event boundary. At that moment. Afterwards, with As the inner integration step size of the target, ensure that the integration step size does not cross the event boundary; S52. Determine if a power flow update has been triggered: Set the next power flow update time as ,like The system determines that a power flow update is triggered within the time interval and adjusts the initial inner-layer integration step size accordingly. The corrected step size is used as the target inner integral step size, so that the integration is exactly advanced to the time of power flow update.

[0040] S53. If neither the state discrete event nor the power grid flow update is triggered, then the initial inner-layer integration step size will be adjusted. Directly determined as the inner integration step size of the target .

[0041] Through the above sub-steps, step S5 can proactively detect events and accurately locate the time of event occurrence before each inner integration step is executed, thereby ensuring that no critical discrete events are missed during the simulation process.

[0042] S6. Perform inner integration: Use the target inner integration step size. and first derivative Second derivative and third derivative Based on the overall dynamic simulation model, the multi-energy system is calculated at time t. System state variables and update the system state variables; set the inner integral counter. The value is increased by one; the simulation time is defined as follows after the update. The updated simulation time is used as the new current simulation time. This will be used as a reference for subsequent steps; then proceed to step S9.

[0043] Multi-energy system at all times System state variables Calculate using the following formula: ; S7. Perform outer layer projection: When step S3 determines the inner layer integration counter... The value reaches the inner integral number At this point, it indicates that a sufficient number of inner-layer small-step integrations have been completed, and the rapidly changing components in the system have been sufficiently refined and suppressed. At this point, the evolution trend of slow dynamics can be extrapolated through outer-layer projection. This is based on the system state variables at the current simulation time. value and at the moment value The number of projections is the number of outer projections. Extrapolation calculations are performed to obtain the outer layer projection result; the inner layer integrator counter is then used. Set to zero.

[0044] The outer projection result is calculated using the following formula: ; In the formula, This is the result of the outer projection. The meaning of this formula is: using the change in state variables from the most recent inner integral. Assuming this trend is the current trend of change in the system, let's assume that this trend will continue in the future. The value remains constant within a certain step size, thus allowing for one-step extrapolation. The state at any given moment.

[0045] This projection extrapolation does not require recalculating derivatives or solving algebraic equations; it only requires one vector subtraction and multiplication operation, resulting in extremely low computational cost. This is a key step in achieving efficient simulation in this invention. The inner layer integrator counter... Set it to zero to prepare for the next round of inner-layer integration.

[0046] S8. Verify the validity of the outer projection: Determine the validity of the multi-energy system within the time interval. Whether a state discrete event or a power grid flow update event is triggered internally includes the following sub-steps: S81. Determine if a state discrete event has been triggered: No. The boundary of the discrete event for each state variable is: ,exist The criterion for discrete events in an internally triggered state is: ; In the formula, For the current simulation moment Next The values ​​that a state variable can take. To be based on the outer projection step size The estimated value after implementation; S82. Determine if a power flow update has been triggered: Set the next power flow update time as ,like The system determines that a power flow update is triggered within the time interval. S83. If either event in step S81 or step S82 is triggered, it indicates that the outer projection step size is too large, spanning the time of the event occurrence. The projection result is unreliable and must be discarded. Return to step S4, starting from the current time. Restart by precisely advancing to the event moment using inner integrals with small steps.

[0047] S84. If neither the discrete state event nor the power grid flow update is triggered, it indicates that the outer projection is effective, the system state is stable within the time interval, and there is no discrete event interference. At this point, accept the outer projection result obtained in step S7 and update the system state variables using the following formula: ; The simulation time after the definition is updated is The updated simulation time is used as the new current simulation time. This will be used as a reference for subsequent steps. Then proceed to step S9.

[0048] S9. Determine the simulation termination condition: Determine the current simulation time. Has the preset simulation end time been reached? If so, terminate the simulation; otherwise, return to step S3 and continue the next round of integration calculation.

[0049] Simulation process derivation example To facilitate understanding of the technical solution of this invention, the execution flow of this invention will be described below with reference to steps S1 to S9 using a simplified deductive process. Some parameters in this example are exemplary values ​​and do not constitute a limitation on the scope of protection of this invention.

[0050] The simulation start time is set to 0 seconds, the simulation end time is set to 86400 seconds, and the inner layer integral is... The value is 3, representing the number of outer projections. The value is 10. Assume the current inner layer integral counter... The value is 2.

[0051] First round of the cycle At the current simulation moment Seconds, execute step S3: Determine Not yet reached Therefore, step S4 is executed.

[0052] In step S4, the system state variables are calculated based on the overall dynamic simulation model. At the current simulation moment The first, second, and third derivatives of the second are calculated, and the initial inner-layer integration step size is obtained based on the third derivative. Second.

[0053] In step S5, it is determined that the multi-energy system has not triggered a state discrete event or a power flow update event within the time interval (10.0, 10.5] seconds, therefore the initial inner-layer integration step size is adjusted. The second is directly determined as the inner integration step size of the target. Second.

[0054] In step S6, the target inner layer integration step size is adopted. Calculate the system's state variables at time 10.5, using seconds and derivatives of all orders. This state includes the gas pressure of each micro-element in the pipeline. and gas flow rate Voltage amplitude and phase angle at each grid node, and state of charge of electric vehicles at each fast charging station. And physical quantities such as the hydrogen pressure at the anode of the fuel cell. Update system state variables, inner integral counter Increment by 1 to 3, define the updated simulation time as 10.5 seconds, and use this updated simulation time as the new current simulation time. Seconds. Then proceed to step S9.

[0055] In step S9, the current simulation time If the simulation has not reached its end time of 86400 seconds, return to step S3.

[0056] Second round of cycling At the current simulation moment Seconds, execute step S3: Determine Achieved Therefore, step S7 is executed.

[0057] In step S7, based on the system state variables at the current time... The value of seconds and at the end of the previous inner integral. The value of seconds The number of projections is Extrapolation calculation yields the outer projection result. The inner layer integrator counter Set to zero.

[0058] In step S8, it is determined that the multi-energy system did not trigger any events within the time interval (10.5, 15.5] seconds, therefore the outer projection result is accepted. As the system state variable of the multi-energy system at time 15.5 seconds This completes the update of the system state variables. The updated simulation time is defined as 15.5 seconds, and this updated simulation time is used as the new current simulation time. Seconds. Then proceed to step S9.

[0059] In step S9, the current simulation time If the simulation has not reached its end time of 86400 seconds, return to step S3.

[0060] Third round of cycling At the current simulation moment Seconds, execute step S3: At this time Not yet reached Therefore, step S4 is executed to begin a new round of inner-layer integration, i.e., from... Starting from the second, a new, fine-grained simulation calculation with small steps is performed.

[0061] This process is repeated continuously. The rapid dynamic process is analyzed in detail through inner-layer integration, and the slow dynamic evolution trend is extrapolated by outer-layer projection with large step size until the current simulation time reaches the preset simulation end time of 86400 seconds. Finally, the trajectory of the changes of each state variable of the multi-energy system during the complete simulation period is obtained.

[0062] Additional examples of event triggering In the above loop process, if in a certain round when step S5 is executed, it is determined that within the time interval... If a discrete event is triggered, causing the state of charge of an electric vehicle at a fast charging station to drop to a charging threshold, then the precise trigger time of this event needs to be solved. and with The step size is adjusted to obtain the target inner layer integration step size. In step S6, the process is precisely advanced to the event moment using the adjusted step size, thereby ensuring the accuracy of event capture.

[0063] Similarly, if it is determined in step S8 that the time interval is within... If an event is triggered within the inner layer, the outer layer projection is deemed invalid, and the process returns to step S4 to re-execute the inner layer integration, ensuring that no critical events are skipped due to the large step size projection.

[0064] Application Examples and Effect Verification The following specific example will be used to verify and explain the technical effect of the quantized state projection integral simulation method for multi-energy systems with electro-hydrogen coupling fast charging stations proposed in this invention.

[0065] Case settings The correctness and effectiveness of the algorithm were verified by a joint simulation of a 20-node hydrogen network and an IEEE 33-node power grid. The simulation system was configured with 5 electro-hydrogen coupling fast charging stations. Figure 2 The diagram shows the topology of a 20-node hydrogen network, which consists of 20 nodes and 19 pipelines. Nodes 1 and 2 are hydrogen source terminals, responsible for injecting hydrogen into the pipeline network. Each of pipelines 8-9 and 17-18 is equipped with a compressor, which operates in constant compression ratio mode (compression ratio 1.05) and constant output mode (output pressure 2.5MPa), respectively. Nodes 6, 9, 15, 18, and 19 are connected to 5 electro-hydrogen coupling fast charging stations, serving as hydrogen load nodes.

[0066] Figure 3 This is a topology diagram of the IEEE 33-node power grid. Five electric-hydrogen coupled fast charging stations are connected to grid nodes 21, 31, 10, 24, and 27, respectively, and are coupled one-to-one with gas grid nodes 9, 18, 6, 15, and 19. Each electric-hydrogen coupled fast charging station simultaneously draws electricity from the grid to charge electric vehicles and draws hydrogen from the gas grid to supply fuel for fuel cells, achieving deep coupling of electricity, hydrogen, and transportation.

[0067] Each electric-hydrogen coupling fast charging station is equipped with two types of charging piles: a standard fast charging pile with a charging power of 60kW and a super-fast charging pile with a charging power of 480kW. Each electric vehicle has a rated capacity of 40kWh, corresponding to a full charge time of 40 minutes for the two types of charging piles and 5 minutes for the two types of charging piles.

[0068] The parameters of each pipe in the hydrogen network are shown in Table 1. The friction coefficient of all pipes is 0.003, the angle between the pipes and the horizontal direction is 0°, and the speed of sound in hydrogen is 1290 m / s. The operating parameters of the compressor are listed in Table 1.

[0069] Table 1 Hydrogen network parameters

[0070] The line parameters of the IEEE 33-node power grid are shown in Table 2.

[0071] Table 2 Parameters of the IEEE 33-node case

[0072] The parameters of the fuel cells in each electro-hydrogen coupling fast charging station are shown in Table 3.

[0073] Table 3 Fuel Cell Parameters

[0074] Simulation settings To verify the effectiveness of the method of the present invention, four different methods were used for comparative simulation: (1) Benchmark method: explicit Runge-Kutta (4,5) formula (RKF45). This method is a mature and general numerical integration method that calculates with a very small fixed step size and uses the result as the accuracy benchmark. (2) Comparison with Method 1: Modified third-order quantized state system (MQSS3), which only uses the quantized state mechanism for adaptive step size control and has no outer projection; (3) Comparison Method 2: Explicit Projective Integration Method (EPIM), which only uses a combination of inner fine integration and outer projection extrapolation, without a quantization state event localization mechanism; (4) The method of the present invention: namely, the quantization state projection integral simulation method of the multi-energy system with electric hydrogen coupling fast charging station in this embodiment, which combines the dual advantages of quantization state system and projection integral algorithm.

[0075] The simulation started at 0 seconds and ended at 86,400 seconds (24 hours). The relevant parameter settings for the method of this invention and the comparative method two are as follows: the air pressure quantum value is 0.5, the air network flow quantum value is 0.0001, the charging power and the number of charging vehicles quantum values ​​are 0.0001, the inner layer integral number is 5, and the outer layer projection number is 10.

[0076] Simulation Results and Analysis Table 4 summarizes the simulation time and accuracy comparison of the four methods.

[0077] Table 4 Simulation Results

[0078] As shown in Table 4, within the same simulation period (0~86400 seconds), the simulation times for the four methods are as follows: RKF45 takes 5636.07 seconds, MQSS3 takes 3840.71 seconds, EPIM takes 3283.62 seconds, and the method of this invention takes 2052.74 seconds. The simulation speed of the method of this invention is approximately 2.75 times that of the baseline method RKF45, approximately 46.5% faster than MQSS3, and approximately 37.5% faster than EPIM.

[0079] In terms of accuracy, based on the results of RKF45, the average relative error of the gas pressure of the method of this invention is 1.4336 × 10⁻⁶. -7 The accuracy falls between MQSS3 and EPIM, belonging to the same order of magnitude; the average relative error of the voltage also falls between the two comparison methods. This indicates that the method of the present invention maintains good simulation accuracy while significantly improving simulation speed.

[0080] Figure 4 The curves of hydrogen pressure versus time at node 12 of the gas network, obtained by four different methods, are presented. Figure 5 The voltage variation curves of grid node 21 over time obtained by four methods are presented. As can be seen from the figures, the pressure and voltage curves obtained by the four methods basically overlap and show a consistent trend, intuitively verifying the correctness of the method of this invention.

[0081] Figure 6 The curves showing the relative pressure error of gas network node 12 over time for MQSS3, EPIM, and the method of this invention relative to the benchmark method RKF45 are presented. Figure 7 The relative error of the grid node 21 voltage relative to RKF45 using three methods is presented as a function of time. From the temporal distribution of the error, the error of the method presented in this invention remains consistently within a low range during the simulation, without any accumulation or divergence of error, indicating that the method of this invention has good numerical stability.

[0082] Summary Table 4 Figures 4 to 7The results show that the proposed quantized state projection integral simulation method for multi-energy systems including electro-hydrogen coupled fast charging stations has a significant simulation speed advantage over existing technologies within a certain relative error tolerance range. This advantage mainly stems from the following three aspects: First, by combining inner-layer integration with outer-layer projection, a dual-layer time-stepping strategy is used to replace a large number of small-step integrations with large-step projections during periods of smooth system change, significantly reducing the number of calculations; Second, by using a quantized state adaptive step-size control mechanism based on the third derivative, the inner-layer integration step size can be automatically adjusted according to the severity of local system changes, avoiding over-computation in traditional fixed-step methods during periods of smooth change; Third, by using inner and outer-layer event detection and precise location mechanisms, the accuracy of discrete event processing is ensured while avoiding redundant calculations caused by improper event processing.

[0083] Therefore, the present invention adopts the above-mentioned quantitative state projection integral simulation method for multi-energy systems with electric hydrogen coupling fast charging stations, which can efficiently and accurately solve the dynamic simulation problem of multi-energy systems with electric hydrogen coupling fast charging stations. It has important engineering application value for the planning, design and operation control of electric hydrogen coupling fast charging stations.

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A quantitative state projection integral simulation method for a multi-energy system including an electro-hydrogen coupling fast charging station, characterized in that, Includes the following steps: S1. Simulation Initialization: Based on the selected multi-energy system including the electric-hydrogen coupling fast charging station, determine the grid parameters, hydrogen network parameters, electric vehicle fast charging station parameters, fuel cell parameters, and simulation control parameters; the simulation control parameters include the inner layer integral number. and outer projection number ;Inner layer integrator counter Set to zero; S2. Establish a system-wide dynamic simulation model: Establish a dynamic simulation model of the multi-energy system, including a power grid flow model, a gas pipeline transmission model, an electric vehicle fast charging station model, and a fuel cell model; combine the above models to form a system-wide dynamic simulation model of the multi-energy system, which includes a system of differential equations and a system of algebraic equations; define the system state variables. and system control variables The system differential equations are used to describe the system state variables. Relationship changing over time; S3. Determine the current state of the inner layer integrator counter: Determine the current state of the inner layer integrator counter. Does the value reach the inner integral number? If the condition is met, proceed to step S7. Step S4 has not been reached; S4. Calculate the derivative and preliminary integration step size: Based on the overall dynamic simulation model, calculate the derivative and preliminary integration step size at the current simulation time. Below, system state variables first derivative Second derivative and third derivative And based on the third derivative, a preliminary inner-layer integration step size is calculated. ; S5. Determine the target inner-layer integration step size: Determine the multi-energy system's time interval. Does the internal state discrete event or power flow update event trigger? If any event is triggered, the initial inner integration step size should be adjusted according to the time of the event. The corrected step size is then determined as the target inner-layer integration step size. ; If no event is triggered, the initial inner integration step size will be... Directly determined as the inner integration step size of the target ; S6. Perform inner integration: Use the target inner integration step size. and first derivative Second derivative and third derivative Based on the overall dynamic simulation model, the multi-energy system is calculated at time t. System state variables and update the system state variables; set the inner integral counter. The value is increased by one; the simulation time is defined as follows after the update. The updated simulation time is used as the new current simulation time. For reference in subsequent steps; then proceed to step S9; S7. Perform outer projection: Based on the system state variables at the current simulation time... value and at the moment value The number of projections is the number of outer projections. Extrapolation calculations are performed to obtain the outer layer projection result; the inner layer integrator counter is then used. Set to zero; S8. Verify the validity of the outer projection: Determine the validity of the multi-energy system within the time interval. Does the internal state discrete event or power flow update event trigger? If any event is triggered, return to step S4; If no event is triggered, accept the outer projection result and use the outer projection result as the time of the multi-energy system. The system state variables are used to update the system state variables in the overall dynamic simulation model; the updated simulation time is defined as... The updated simulation time is then used as the new current simulation time. For reference in subsequent steps; then proceed to step S9; S9. Determine the simulation termination condition: Determine the current simulation time. Has the preset simulation end time been reached? If it has, terminate the simulation; otherwise, return to step S3.

2. The quantized state projection integral simulation method for a multi-energy system including an electro-hydrogen coupling fast charging station according to claim 1, characterized in that, In step S1: Power grid parameters include network topology, branch resistance, and branch reactance; Hydrogen network parameters include pipe length, pipe diameter, pipe friction coefficient, pipe angle with the horizontal direction, sound velocity in hydrogen, compressor operating parameters, and pipe micro-segment length. The parameters for electric vehicle fast charging stations include road traffic flow, charging pile charging power, nodal electricity price, and charging vehicle battery level. Fuel cell parameters include battery operating temperature, maximum battery current density, proton exchange membrane internal resistance, proton membrane thickness, battery area, number of cells in series, anode capacity, anode channel outlet orifice coefficient, and supply pipe outlet orifice coefficient. The simulation control parameters also include simulation start time, simulation end time, and quantum value.

3. The quantized state projection integral simulation method for a multi-energy system including an electro-hydrogen coupling fast charging station according to claim 1, characterized in that, In step S2, the overall dynamic simulation model is composed of the following models: S21. Power Flow Model: Ignoring transient processes in the power grid, an AC power flow calculation model is adopted. S22. Gas Pipeline Transport Model: The hydrogen pipeline space is discretized into several pipeline micro-elements. For each pipeline micro-element, the partial differential equation describing gas transport is transformed into an ordinary differential equation using the method of characteristics. The transport equation for a small element of a pipe segment is: ； ； In the formula, For the first The gas pressure of a micro-element in a section of the pipeline. For the first Gas flow rate of a micro-element in a pipeline segment The speed of sound in hydrogen gas. The cross-sectional area of ​​the pipe. This is the pipe friction coefficient. For the pipe diameter, It is the acceleration due to gravity. The angle between the pipe and the horizontal direction. and Let be the difference functions along the positive and negative characteristic lines, respectively, defined as: ； ； In the formula, Let the length of the pipe element be denoted as . For the spatial coordinate variables along the pipeline, For the first Spatial coordinates of the center point of the micro-element of the pipeline segment. These are general physical quantity symbols used when calculating pressure equations. Specifically refers to When calculating the flow equation, Specifically refers to ; and The first Section and the General physical quantities on a segment of pipe micro-element; S23. Electric Vehicle Fast Charging Station Model: The differential equation for the electric vehicle charging process is: ； In the formula, The charging power of the fast charging station The state of charge (SOC) of an electric vehicle; The number of vehicles charging is determined by the current traffic flow and charging threshold. The current battery level of vehicles on the road section follows a normal distribution. Vehicles with a battery level below the charging threshold enter the fast charging station for charging. Each fast charging station connects to a distribution network node that uses dynamic electricity pricing. The non-linear electricity pricing function relationship between the node voltage and the charging price is as follows: ； In the formula, For nodes The charging price, For nodes voltage, , The coefficients of the electricity price function; The piecewise linear relationship between user charging threshold and nodal electricity price is as follows: ； In the formula, For nodes The charging threshold, This is the upper limit of the charging threshold. This is the lower limit of the charging threshold. , Electricity price parameters; S24. Fuel cell model: including voltage power model and hydrogen reaction flow channel model; In the voltage-power model, the fuel cell stack consists of It is composed of identical single cells connected in series, and the voltage of a single cell is... for: ； fuel cell voltage for: ； fuel cell output power for: ； Fuel cell net output power for: ； In the formula, This is the thermodynamic potential of the battery. To activate the polarization overpotential, For concentration polarization overpotential, For Ohm overpotential, For fuel cell current, The power consumed by the air compressor that supplies oxygen to the cathode; The differential equation for the hydrogen reaction flow channel model is: ； In the formula, Here is the molar mass of hydrogen. For anode capacity, The gas constant is Battery operating temperature This refers to the hydrogen gas pressure at the anode of the fuel cell. , , These represent the anode inlet, outlet, and consumed hydrogen mass flow rates, respectively. S25. By combining the power grid flow model, gas pipeline transmission model, electric vehicle fast charging station model, and fuel cell model, the standard form of the overall dynamic simulation model is obtained: ； In the formula, For system state variables, For system control variables, The system consists of a set of differential equations. For the system of algebraic equations, System state variables The first derivative with respect to time, .

4. The quantized state projection integral simulation method for a multi-energy system including an electro-hydrogen coupling fast charging station according to claim 1, characterized in that, In step S4, the first derivative Second derivative and third derivative The calculation formula is: ； ； ； In the formula, For system control variables, For the system control variables at the current simulation time The value, The system consists of a set of differential equations. , These are the first and second derivative expressions of the system's differential equations, respectively.

5. The quantitative state projection integral simulation method for a multi-energy system including an electro-hydrogen coupling fast charging station according to claim 1, characterized in that, In step S4, the initial inner layer integration step size is determined. Calculate using the following formula: ； In the formula, For the quantum value of the state variable, For the system state variables at the current simulation time The third derivative of .

6. The quantized state projection integral simulation method for a multi-energy system including an electro-hydrogen coupling fast charging station according to claim 1, characterized in that, Step S5 includes the following sub-steps: S51. Determine if a state discrete event has been triggered: No. The boundary of the discrete event for each state variable is: ,exist The criterion for discrete events in an internally triggered state is: ； In the formula, For the current simulation moment The next The values ​​that a state variable can take. To integrate according to the initial inner layer step size The estimated value after implementation; If a discrete state event is triggered, the step size that satisfies the following equation is calculated. : ； and with As the inner integration step size of the target; In the formula, These are the current simulation times. Next The first, second, and third derivatives of each state variable; S52. Determine if a power flow update has been triggered: For the next power grid flow update time, if The system determines that a power flow update is triggered within the time interval and adjusts the initial inner-layer integration step size accordingly. The corrected step size is used as the target inner layer integration step size; S53. If neither the state discrete event nor the power grid flow update is triggered, then the initial inner-layer integration step size will be adjusted. Directly determined as the inner integration step size of the target .

7. The quantitative state projection integral simulation method for a multi-energy system including an electro-hydrogen coupling fast charging station according to claim 1, characterized in that, In step S6, the multi-energy system at time System state variables Calculate using the following formula: 。 8. The quantitative state projection integral simulation method for a multi-energy system including an electro-hydrogen coupling fast charging station according to claim 1, characterized in that, In step S7, the outer projection result is calculated using the following formula: ； In the formula, This is the result of the outer projection.

9. The quantitative state projection integral simulation method for a multi-energy system including an electro-hydrogen coupling fast charging station according to claim 1, characterized in that, Step S8 includes the following sub-steps: S81. Determine if a state discrete event has been triggered: No. The boundary of the discrete event for each state variable is: ,exist The criterion for discrete events in an internally triggered state is: ； In the formula, For the current simulation moment Next The values ​​that a state variable can take. To be based on the outer projection step size The estimated value after implementation; S82. Determine if a power flow update has been triggered: For the next power grid flow update time, if The system determines that a power flow update is triggered within the time interval. S83. If any event in step S81 or step S82 is triggered, return to step S4. S84. If neither the state discrete event nor the power grid flow update is triggered, then accept the outer projection result and update the system state variables according to the following formula: ； In the formula, This is the outer projection result obtained in step S7.

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