Distributed robust estimation method for electricity-gas integrated energy system based on time domain model

Abstract

The present invention discloses a distributed robust estimation method for an electric-gas integrated energy system based on a time-domain model. The method first derives a simplified gas grid state-space model based on the time-domain model, with node pressure as the state variable. It then establishes a grid state-space model and a coupling element model represented by gas turbines and electric hydrogen production. Finally, based on the Kalman filter algorithm, it performs distributed robust state estimation using a distributed estimation strategy with limited boundary information interaction and an adaptive correction algorithm for process noise and measurement noise. The present invention can address the communication privacy issues of multiple management entities between the electric and gas subsystems. By adaptively correcting time-varying noise parameters, it effectively improves state estimation accuracy and suppresses the impact of bad data. Furthermore, after simplifying the gas grid model, computational efficiency is significantly improved, providing real-time data support for the operational control of the integrated energy system.

Description

Technical Field

[0001] The present invention belongs to the field of power system monitoring, analysis and control, and in particular relates to a distributed robust estimation method for an electric-gas integrated energy system based on a time domain model. Background Art

[0002] The deepening coupling between power and natural gas systems has led to the formation of a collaborative, flexible, and efficient integrated electric and gas system (IEGS). This system breaks the traditional model of separate design, planning, and operation of multiple energy systems and plays a significant role in improving energy efficiency, absorbing renewable energy output, and promoting energy conservation and emission reduction. Against this backdrop, the construction of a new energy management system for deeply coupled IEGS has become an inevitable trend. State estimation, as the cornerstone of energy management systems, provides data support for subsequent IEGS power flow calculations, security assessments, and optimized scheduling. Therefore, accurate and real-time IEGS state estimation is of great significance.

[0003] Because traditional steady-state modeling of gas grids is only suitable for estimating grid states over longer timescales and is incapable of tracking the grid's real-time operating state during short-term load fluctuations, appropriate dynamic modeling of gas grids is needed. The dynamic characteristics of natural gas transmission in pipelines follow the laws of fluid mechanics and are typically described by a set of partial differential equations governing mass and momentum conservation, which are difficult to solve directly using analytical methods. Currently proposed simplified gas grid models include finite element models, "pipe-storage" models, and unified energy path models. Existing IEGS state estimation research often uses finite element difference models to describe the dynamic characteristics of gas grids. This model requires the introduction of redundant spatiotemporal elements, making it difficult to balance state estimation accuracy and computational complexity. Most studies fail to consider the privacy and security of communications between the electrical and gas subsystems, and the estimation algorithms employed lack robustness. Therefore, appropriate IEGS state estimation methods are urgently needed to provide technical support for the safe and stable operation of IEGS. Summary of the Invention

[0004] The purpose of this invention is to address the problems of low computational efficiency and insufficient robustness in existing IEGS dynamic state estimation research. This invention provides a distributed robust estimation method for an electric-gas integrated energy system based on a time-domain model, improving computational efficiency while ensuring accuracy. Based on the time-domain model, the gas grid state space equations with node pressure as the state variable are derived to simplify and reduce the dimensionality of the gas grid model. Using the Kalman filter algorithm as a framework, a distributed SE is established using the interaction of finite boundary information to address the issue of multiple management entities between different subsystems. Adaptive correction methods for process noise and measurement noise are used to accurately track time-varying noise parameters, ensuring the robustness of the proposed method.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a distributed robust estimation method for an electric-gas integrated energy system based on a time domain model, comprising the following steps:

[0006] S1. Based on the electricity-gas integrated energy system, obtain the gas network information and the power grid information in the system respectively;

[0007] S2. Based on the gas network information, the boundary conditions and initial conditions of each branch in the gas network information are used as input, and the terminal state quantity of each branch is used as output to construct a time domain model of the gas network branch;

[0008] S3. Add natural gas network topology constraints to the branch time-domain model and construct the network time-domain model using a matrix partitioning method. S4. Based on the gas network branch time-domain model and the network time-domain model, obtain the state equations for the node pressures at the current and previous moments, and obtain the measurement equations for the current node pressure, the current node injection flow, and the flow at the beginning and end of the branch. Then, based on the state equations and measurement equations, construct the gas network state space model.

[0009] S5. Based on the grid information, the grid state equation is constructed using the Holt two-parameter exponential smoothing method, and the grid state space model is constructed in combination with the grid measurement equation; a coupling element model is constructed based on the energy conversion relationship between the gas turbine and the electric hydrogen production unit;

[0010] S6. Based on the gas grid state space model, the power grid state space model, and the coupling element model, and based on the Kalman filter algorithm, a distributed robust state estimation model for the electric-gas integrated energy system is constructed using a distributed estimation strategy with limited boundary information interaction, combined with a process noise adaptive correction algorithm and a measurement noise adaptive correction algorithm;

[0011] According to the grid state space model, a grid state estimation model is constructed based on the Kalman filter algorithm and combined with the process noise and measurement noise adaptive correction algorithm;

[0012] S7. Determine whether electricity and gas collaborative state estimation needs to be performed at the current moment based on the electricity and gas state estimation execution cycle. If so, perform state estimation using the distributed robust state estimation model of the electricity-gas integrated energy system and output a state value. Otherwise, perform state estimation using the power grid state estimation model and output a state value.

[0013] S8. Determine whether the current time is the preset end time. If so, use the status value output in step S7 as the result. Otherwise, update the current time according to the preset value and return to step S7.

[0014] Compared to existing technologies, this invention offers two significant advantages: First, it proposes a simplified gas grid state-space model based on a time-domain model. This model addresses the large computational scale of traditional finite element differential models while ensuring computational accuracy. Furthermore, it introduces a dynamic distributed strategy and a noise-adaptive algorithm to propose a distributed robust state estimation method for an integrated electric-gas energy system. This method effectively improves estimation accuracy and suppresses the impact of bad data while protecting subsystem privacy. Its computational efficiency far exceeds that of traditional differential methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Flow chart of the method of the present invention.

[0016] Figure 2 This is the topological structure diagram of the electricity-gas integrated energy system.

[0017] Figure 3 is the voltage amplitude estimation result of grid node 1.

[0018] Figure 4 This is the pressure estimation result of gas network node 5.

[0019] Figure 5 is the RMS error of grid coupling measurement picture.

[0020] Figure 6 is the root mean square error of the gas-grid coupling measurement picture.

[0021] Figure 7 This is the estimation result diagram when the measurement of grid node 10 is lost.

[0022] Figure 8 This is the estimation result diagram under the measurement loss of gas grid node 16. DETAILED DESCRIPTION

[0023] In order to better understand the technical content of the present invention, specific embodiments are given and described below with reference to the accompanying drawings.

[0024] The proposed model is constructed by using the IEEE 24-node power system and the modified 20-node Belgian natural gas system to construct the IEGS-SE case study, which includes 39 transmission lines, 21 pipelines and 2 compressor stations. The IEGS is coupled through 1 GT and 1 P2G. The system topology is as follows: Figure 2 shown.

[0025] The method flow of the present invention is as follows Figure 1 The distributed robust estimation method of the electric-gas integrated energy system based on the time domain model includes the following steps:

[0026] S1. Based on the electricity-gas integrated energy system, obtain the gas network information and power grid information in the system respectively.

[0027] The grid information includes: grid topology information, capacitance of each node to ground, impedance and capacitance of each branch to ground, and execution period Δt of grid state estimation. e And power grid measurement information; gas network information includes: each pipeline length, inner diameter, friction coefficient, average flow velocity, gas sound velocity, gas network state estimation execution period Δt g , differential space step Δx g , energy conversion coefficient of coupling elements and gas network measurement information.

[0028] Then the program is initialized: the initial values of the process noise and state estimation covariance, the boundary information interaction convergence threshold, the forgetting factor of the process noise adaptive algorithm, and the correction threshold of the measurement noise adaptive algorithm are set.

[0029] S2. Based on the gas network information, the boundary conditions and initial conditions of each branch in the gas network information are used as input, and the terminal state quantity of each branch is used as output to construct a time domain model of the gas network branch.

[0030] Specifically, it includes the following steps S2.1 to S2.5:

[0031] S2.1. When natural gas is transported in a pipeline in one dimension isothermally, the two main laws of conservation of mass and conservation of energy are satisfied. The internal characteristics of the natural gas pipeline can be described as a set of linear partial differential equations, as shown below:

[0032]

[0033] Where p is the gas pressure of natural gas, q is the gas flow rate of natural gas; v a is the gas sound velocity; S, D, and λ are the cross-sectional area, inner diameter, and friction coefficient of the pipe, respectively; w is the average flow velocity in the pipe; g and θ are the gravitational acceleration and the pipe inclination. This linear partial differential equation system is converted into a unified linear partial differential equation as follows:

[0034]

[0035] Among them, u is the gas network state quantity, which is gas pressure p and flow q respectively, T is the transpose sign; K1 and K2 are constant coefficient matrices, as shown in the following formula:

[0036]

[0037] S2.2. Use the central difference quotient and implicit difference scheme to convert the unified linear partial differential equation into an algebraic equation for approximate solution, as shown below:

[0038]

[0039]

[0040]

[0041]

[0042] Among them, i and t are the spatial grid number and the time grid number respectively, μ 1-3 is a constant coefficient matrix, Δt g is the gas grid state estimation execution cycle, i.e., the differential time step; Δx g is the difference space step size, E is the second-order unit matrix, S2.3, based on the algebraic equation in step S2.2, construct the relationship between the state quantities of the adjacent time section branches:

[0043]

[0044] in, and are the branch state quantities at time t-1 and time t, respectively, where is relative to Initial conditions; is the boundary condition at time t, including the state quantity of the branch head end at time t-1 and time t; M is the number of branch space difference segments; χ and ε are constant coefficient matrices with dimensions of M×M and M×2, respectively, expressed as:

[0045] in,

[0046] S2.4, the boundary conditions in Merge to initial conditions In the process, construct the terminal state of the branch at time t The function expression is:

[0047]

[0048] Where, is the state quantity of the branch terminal at time t; α and β are the transfer matrices of the adjusted boundary conditions and initial conditions, respectively. S2.5. For each branch in the natural gas network, the state quantity u is represented by gas pressure p and flow q. The time domain model of the gas network branch is obtained by reclassification and sorting, as follows:

[0049]

[0050] in, is the N-dimensional column vector of the gas pressure and gas composition at the beginning and end of the branch; α1, α2, α3 and α4 are the N×N-dimensional transfer matrices of the state quantity at the beginning to the state quantity at the end; N-dimensional column vector of initial conditions to terminal state quantities.

[0051] It can be seen that in step S2.5, the input is the boundary conditions and initial conditions, and the output is the state quantity of the branch end, which constitutes the time domain model of the gas network branch.

[0052] S3. Add natural gas network topology constraints to the branch time domain model and use the matrix block method to construct the network time domain model, including the following steps S3.1 to S3.3

[0053] S3.1. To construct a natural gas network time-domain model, it is necessary to add topological constraints to the branch time-domain model. This mainly considers the conservation of node injection flow and the fact that the pressure at the beginning and end of a branch is equal to the pressure at the node. Therefore, based on the conservation of node injection flow and the fact that the pressure at the beginning and end of a branch is equal to the pressure at the node, the natural gas network topological constraints are added to the branch time-domain model as follows:

[0054]

[0055]

[0056] in, Inject traffic into the node; is the pressure at each node; A in and A out A is the node-branch inflow and outflow association matrix; pn1 and A pn2 is the branch-end node association matrix;

[0057] S3.2, the branch time domain model is extended to the entire network, and the branch time domain model is transformed into a node pressure p using the matrix block idea. 0 / M Characterize the flow rate at the beginning and end of the branch q 0 / M The function expression is as follows:

[0058]

[0059] Among them, K 11 , K 12 , K 21 , K 22 is an N×N dimensional constant coefficient matrix; is an N-dimensional column vector;

[0060] S3.3. Combine the network topology of step S3.1 and the function expression of step S3.2 to construct the network time domain model as follows:

[0061]

[0062] Among them, Y n is the generalized admittance matrix of the natural gas network; b t is the equivalent component determined by the system state at the previous moment, Y n and b t The analytical expression is as follows:

[0063] Y n =(A in K 21 -A out K 11 )A pn1 +(A in K 22 -A out K 12 )A pn2 ,

[0064]

[0065] S4. Based on the gas network branch time-domain model and the network time-domain model, obtain the state equations for the node pressure at the current moment and the previous moment, and obtain the measurement equations for the current node pressure, the current node injection flow, and the branch head and end flow. Then, based on the state equations and the measurement equations, construct the gas network state-space model. The gas network state-space model mainly includes two parts: the state equation and the measurement equation. The key to constructing the state equation is to derive the functional relationship between the state quantity at the current moment and the previous moment. The following steps are included: S4.1 to S4.5:

[0066] S4.1. In the time domain model of the gas network branch The functional relationship with the node pressure at the previous moment is expressed as follows:

[0067]

[0068] Among them, β1, β2, β3, and β4 are the state quantities of the head end. The N×N dimensional transfer matrix; For the remaining state pairs N-dimensional transfer column vector;

[0069] S4.2, for step S3.3 b t The analytical expression of is rewritten as follows:

[0070]

[0071] Among them, K 31 , K 32 and Y b is an N×N dimensional constant coefficient matrix, Transfer component for the state of the previous moment;

[0072] S4.3. According to the network time domain model, b t Substituting the analytical expression of into the network time domain model, we get the following expression:

[0073]

[0074] The gas network state equation is further obtained as follows:

[0075]

[0076] Among them, F g and is the state transfer matrix and control variable of the gas network. During the calculation process, F g is a constant coefficient matrix related to pipeline parameters and operating characteristics; The flow injected by each node at the current moment Its state transfer component at the previous moment Related, F g and Obtained through offline calculation, The prediction is obtained by Holt's two-parameter exponential smoothing method;

[0077] S4.4. Measure the node pressure p according to the gas network volume n , node injection traffic q n and the branch head and end flow q 0 / M , the measurement equation for constructing the gas network is as follows:

[0078]

[0079] S4.5. Construct the state space model of the gas network based on the state equation and measurement equation, as follows:

[0080]

[0081] in, is the gas network state quantity, For gas network quantity measurement; H g and It is the gas network measurement coefficient matrix and system state transfer component; is the process noise vector and is the measurement noise vector and

[0082]

[0083] S5. Based on the grid information, the grid state equation is constructed using the Holt two-parameter exponential smoothing method. The grid state space model is constructed by combining the grid measurement equations. A coupling element model is constructed based on the energy conversion relationship between the gas turbine and the hydrogen production unit. This includes the following steps S5.1 to S5.2:

[0084] S5.1. According to the grid state quantity: node voltage amplitude V i and voltage phase angle θ i , and the state equation of the power grid is established based on the Holt two-parameter exponential smoothing method; according to the power grid quantity measurement: node voltage V i , node injection power P i , Q i And the branch power P ij , Q ij , construct the state space model corresponding to the power grid, as follows:

[0085]

[0086] in, and are the state and quantity measurements of the power grid at time t; Obtained by Holt's quadratic exponential smoothing method; is the power grid measurement equation; is the process noise vector and is the measurement noise vector and

[0087] In an integrated electricity-gas energy system, natural gas and electricity are typically transferred bidirectionally through gas turbines and hydrogen-to-electricity units. Gas turbines burn natural gas to generate electricity, smoothing out grid load fluctuations. Hydrogen-to-electricity units, on the other hand, consume excess electricity to generate natural gas, contributing to energy conservation and emissions reduction.

[0088] S5.2. Based on the energy conversion relationship between the gas turbine and the electric hydrogen generator, the coupling element model is constructed as follows:

[0089]

[0090] Among them, P GT and P P2G The electric power output / consumed by the gas turbine and the electric hydrogen production unit; q GT and q P2G The gas flow rate burned / generated by the gas turbine and the electric hydrogen production unit; η GT and η P2G is the energy conversion coefficient of the gas turbine and the electric hydrogen production unit.

[0091] The distributed estimation strategy employed in this method primarily consists of three steps: prediction, filtering, and boundary information exchange. The prediction and filtering steps perform local estimation of the subsystems. Boundary information exchange uses the estimated values and covariances of coupled measurements after local estimation as boundary information. These are supplemented by the constraint interaction of coupled elements to provide redundant measurements of the other system. The calculation is iterated until the constraints converge. The power grid is a nonlinear system, while the gas grid is a linear system. Extended Kalman and linear Kalman algorithms are used as the local estimation methods for the two subsystems, respectively.

[0092] S6. Based on the gas grid state space model, the power grid state space model, and the coupling element model, and based on the Kalman filter algorithm, a distributed robust state estimation model for the electric-gas integrated energy system is constructed using a distributed estimation strategy with limited boundary information interaction, combined with a process noise adaptive correction algorithm and a measurement noise adaptive correction algorithm; including steps S6.1.1 to S6.1.5:

[0093] S6.1.1. Prediction step: Calculate the predicted values of the power grid and gas grid states and the prediction covariance matrix of the power grid and gas grid according to the following formula:

[0094]

[0095] in, are the estimated state values of the power grid and gas grid at time t-1, and the estimated covariance of the power grid and gas grid respectively; and are the state prediction values of the power grid and gas grid at time t, and the prediction covariance of the power grid and gas grid respectively;

[0096] S6.1.2, Filtering step: Calculate the estimated values of the power grid and gas grid states and the estimated covariance matrix according to the following formula:

[0097]

[0098] in, are the estimated values and covariances of the power grid and gas grid states before interaction of boundary information, respectively; is the state estimated covariance The inverse matrix of is the intermediate vector, where S6.1.3, Boundary Information Interaction: The distributed estimation strategy only has information interaction at the energy level between the power grid and the gas grid, and does not involve state information. Therefore, the boundary information in the electric-gas integrated energy system mainly includes the node injection flow associated with the gas turbine and the electric hydrogen production unit, and the node injection active power estimation value. and the estimated covariance Boundary information interaction is performed according to the following formula:

[0099]

[0100] in, η cp is the energy conversion coefficient set; for The part corresponding to the injection flow of the coupling node of the gas network; The predicted value of active power injected into the grid coupling node. When , where υ is the convergence threshold, the boundary information interaction ends; Inject active power estimation values into the nodes associated with gas turbines and hydrogen production units for the boundary information of the electric-gas integrated energy system. and Inject the active power estimation covariance for the nodes associated with the gas turbine and the hydrogen generator:

[0101]

[0102] In dynamic state estimation, if the process noise variance matrix If the numerical value does not match the prediction accuracy of the state equation, it will cause the filtering error to increase, and even lead to computational pathology in severe cases. This method uses a process noise adaptive algorithm to ensure Q e / g Under the condition of satisfying semi-positive definiteness, the integrity of the correction information is maintained as much as possible to accurately track the time-varying process noise parameters.

[0103] S6.1.4, the process noise adaptive correction algorithm is as follows:

[0104]

[0105] Among them, d t is the weight coefficient; is the difference between the estimated value and the predicted value at time t; is the Kalman gain matrix; is the measurement prediction covariance matrix, which can be expressed as:

[0106]

[0107]

[0108]

[0109]

[0110] Where b is the forgetting factor and 0.95≤b≤0.995.

[0111] S6.1.5, the measurement noise adaptive correction algorithm is as follows:

[0112]

[0113]

[0114]

[0115] in, is the corrected measurement noise variance matrix; is the correction scale matrix; c is the threshold; is the i-th normalized residual component of the measurement prediction value; and is the i-th component of the measurement prediction value and prediction variance matrix.

[0116] Based on the grid state space model, a grid state estimation model is constructed based on the Kalman filter algorithm and combined with the process noise and measurement noise adaptive correction algorithm. It includes steps S6.2.1 to S6.2.4:

[0117] S6.2.1. Calculate the grid state prediction value and prediction covariance matrix according to the following formula:

[0118]

[0119] in, are the estimated value and estimated covariance of the power grid state at time t-1 respectively; and

[0120] are the predicted value and predicted covariance of the power grid state at time t respectively;

[0121] S6.2.2. Calculate the grid state estimate and estimated covariance matrix according to the following formula:

[0122]

[0123] in, are the estimated value and covariance of the power grid state with no boundary information interaction; is the state estimated covariance The inverse matrix of is the intermediate vector, where S6.2.3, the process noise adaptive correction algorithm is as follows:

[0124]

[0125] Among them, d t is the weight coefficient; is the difference between the estimated value and the predicted value at time t; is the Kalman gain matrix; is the measurement prediction covariance matrix, which can be expressed as:

[0126]

[0127]

[0128]

[0129]

[0130] Where b is the forgetting factor and 0.95≤b≤0.995;

[0131] S6.2.4, the measurement noise adaptive correction algorithm is as follows:

[0132]

[0133]

[0134]

[0135] in, is the corrected measurement noise variance matrix; is the correction scale matrix; c is the threshold; is the i-th normalized residual component of the measurement prediction value; and is the i-th component of the measurement prediction value and prediction variance matrix.

[0136] S7. Determine whether it is necessary to perform electricity and gas collaborative state estimation at the current moment based on the electricity and gas state estimation execution cycle. If so, use the distributed robust state estimation model of the electricity-gas integrated energy system to perform state estimation and output the state value. Otherwise, use the power grid state estimation model to perform state estimation and output the state value.

[0137] The current time is updated according to the preset value, and the process returns to step S7.

[0138] S8. Determine whether the current time is the preset end time. If so, use the status value output in step S7 as the result. Otherwise, update the current time according to the preset value and return to step S7.

[0139] The following is a test of the method of the present invention:

[0140] 1) State estimation filter performance test

[0141] The total simulation time is 12 hours, and the execution period of power grid and gas grid state estimation is Δt e , Δt g For 1 minute and 6 minutes, the state estimation is performed under the normal full measurement configuration (i.e. the measurement obeys Gaussian distribution). The state estimation results of the power grid and gas network are as follows: Figure 3 、 4 As shown in the figure, when the measured value of the state quantity of the electric-gas integrated energy system fluctuates around its true value, its estimated value can accurately track the state change.

[0142] Table 1 shows the mean RMS error of the state quantity under different adaptive algorithms in the present invention. As shown in Table 1, the process noise adaptive algorithm enhances the ability to track time-varying noise parameters during the estimation process, effectively improving the filtering performance; while the measurement noise adaptive algorithm has little effect on the overall filtering performance under normal measurement conditions.

[0143]

[0144] Where: F is the number of Monte Carlo simulations; m is the number of state quantities; and are the i-th component of the estimated value and true value of the state quantity respectively; N is the number of time sections.

[0145] Table 1

[0146]

[0147] 2) Distributed Estimation Strategy Performance Test

[0148] When the parameter settings remain unchanged and both noise adaptive algorithms are used, the mean root mean square error of the state quantity of each subsystem is calculated when the state is estimated separately. The voltage amplitude 9.24×10 -4 pu, voltage phase angle 1.71×10 -4 rad, nodal pressure Compared with the performance indicators in Table 1, it can be seen that the distributed strategy adopted by the method proposed in the present invention improves the measurement redundancy of the subsystem through boundary information interaction and improves the overall filtering effect.

[0149] In addition, when the proposed method of the present invention is used to estimate the states of the electric and gas subsystems separately, the root mean square error of the coupled measurements corresponding to the gas turbine and electric hydrogen production unit nodes is For comparison, the simulation results are shown in Figure 5 、 6 It can be seen that the distributed strategy adopted by the method proposed in the present invention can improve the estimation accuracy of the subsystem coupling measurement, and because the estimation accuracy of the power grid itself is relatively high, the estimation accuracy of the gas grid measurement is more significantly improved during information interaction.

[0150]

[0151] Where: m cpis the number of coupled measurements; is the estimated value of the coupling measurement; is the true value of the coupling measurement.

[0152] 3) Robust estimation performance test

[0153] Figure 7 、 8 The state estimation results of the electric-gas integrated energy system under measurement loss in this invention are given. Figure 7 、 8 It can be seen that if the measurement adaptive algorithm is not added, the estimated value corresponding to the lost measurement will deviate significantly from the true value at 4h to 5h; however, the method proposed in the present invention can still better track the system state changes during this period due to the addition of the measurement adaptive algorithm.

[0154] Under the full measurement configuration, the probability of bad data in each subsystem at each time section is 0.5, and the number accounts for 1% to 10% of the subsystem measurement, which is half of the actual measurement size. The bad data scenarios under each ratio are randomly generated, and 500 Monte Carlo simulation experiments are performed, and the mean root mean square error of the state quantity is used. To further evaluate the robustness of the algorithm, the simulation results are shown in Table 2.

[0155] Table 2

[0156]

[0157] As shown in Table 2, as the proportion of bad data increases, the IEGS state quantity It will rise, but it will still be around 10. -4 The fluctuation is about the same as that of the M1 algorithm in Table 1. This is mainly due to the fact that the robust M-estimation theory based on Huber can judge and update the statistical characteristics of the measurement noise in real time during the filtering step of each time section. If suspicious measurement data is found, its impact on the state estimation is reduced. Therefore, the proposed method has good robustness in the face of bad data interference.

[0158] 4) Computational efficiency test

[0159] The online estimation duration of the proposed method consists primarily of three components: the filtering step duration for the power and gas grids, and the boundary information interaction duration. The prediction step for the power and gas grids only involves historical state information or load information, which can be obtained through offline calculations. Table 3 shows the average duration for each step of the electricity and gas collaborative estimation solution on a single time slice using an Intel Core i7-10700 CPU and 16GB of RAM.

[0160] Table 3

[0161]

[0162] Since the gas grid uses a time domain model, it is necessary to calculate the state space model in advance according to the initial conditions of the system, that is, the estimated value of the state quantity at the previous moment, in the prediction step. Therefore, the offline calculation time is long. The state equation of the power grid is directly predicted by the exponential smoothing method, and the calculation process is relatively simple and relatively time-consuming. It is worth noting that the distributed strategy proposed in this paper only uses small-scale coupling boundary information to perform iterative corrections based on the initial filtering step, avoiding the tediousness of re-performing the overall SE of the subsystem, and boundary information convergence can be achieved after 1 to 2 iterations. In summary, the overall online calculation time of the method proposed in this invention is less than 3×10 -3 seconds, which can meet the needs of online real-time applications.

[0163] The above simulation results verify the effectiveness and practicality of the proposed model. This demonstrates that this distributed robust state estimation method for an integrated power-gas energy system based on a time-domain model can effectively track changes in process noise parameters while protecting subsystem privacy, suppress the impact of bad measurement data, and achieve a balanced approach to estimation accuracy and computational efficiency, providing technical support for the real-time scheduling and management of large-scale integrated power-gas energy systems.

[0164] While the present invention has been described above with reference to preferred embodiments, this is not intended to limit the present invention. Persons skilled in the art will readily appreciate that various modifications and variations can be made without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A distributed robust estimation method for electric-gas integrated energy systems based on a time domain model, characterized by: The steps include: S1. Based on the electricity-gas integrated energy system, obtain the gas network information and the power grid information in the system respectively; S2. Based on the gas network information, the boundary conditions and initial conditions of each branch in the gas network information are used as input, and the terminal state quantity of each branch is used as output to construct a time domain model of the gas network branch; S3. Add natural gas network topology constraints to the branch time domain model and use the matrix block method to construct the network time domain model; S4. Based on the gas network branch time domain model and the network time domain model, obtain the state equations for the node pressure at the current moment and the previous moment, and obtain the measurement equations for the current node pressure, the current node injection flow, and the branch head and end flow; then, based on the state equations and measurement equations, construct the gas network state space model; S5. Based on the grid information, the grid state equation is constructed using the Holt two-parameter exponential smoothing method, and the grid state space model is constructed in combination with the grid measurement equation; a coupling element model is constructed based on the energy conversion relationship between the gas turbine and the electric hydrogen production unit; S6. Based on the gas grid state space model, the power grid state space model, and the coupling element model, and based on the Kalman filter algorithm, a distributed robust state estimation model for the electric-gas integrated energy system is constructed using a distributed estimation strategy with limited boundary information interaction, combined with a process noise adaptive correction algorithm and a measurement noise adaptive correction algorithm; According to the grid state space model, a grid state estimation model is constructed based on the Kalman filter algorithm and combined with the process noise and measurement noise adaptive correction algorithm; S7. Determine whether electricity and gas collaborative state estimation needs to be performed at the current moment based on the electricity and gas state estimation execution cycle. If so, perform state estimation using the distributed robust state estimation model of the electricity-gas integrated energy system and output a state value. Otherwise, perform state estimation using the power grid state estimation model and output a state value. S8. Determine whether the current time is the preset end time. If so, use the status value output in step S7 as the result. Otherwise, update the current time according to the preset value and return to step S7.

2. The distributed robust estimation method for the electric-gas integrated energy system based on the time domain model according to claim 1 is characterized in that: Step S1 is specifically as follows: Based on the electricity-gas integrated energy system, obtain gas network information including: length of each pipeline, inner diameter, friction coefficient, average flow velocity, gas sound velocity, gas network state estimation execution period Δt g , differential space step Δx g , the energy conversion coefficient of the coupling element, and the gas network measurement information; the grid information obtained includes: grid topology information, capacitance of each node to the ground, impedance and capacitance of each branch to the ground, and execution period Δt of grid state estimation e , and grid measurement information.

3. The distributed robust estimation method for the electric-gas integrated energy system based on the time domain model according to claim 1 is characterized in that: Step S2 includes the following sub-steps: S2.

1. The internal characteristics of a natural gas pipeline are described as a set of linear partial differential equations, as follows: Where p is the gas pressure of natural gas, q is the gas flow rate of natural gas; v a is the gas sound velocity; S, D, and λ are the cross-sectional area, inner diameter, and friction coefficient of the pipe, respectively; w is the average flow velocity in the pipe; g and θ are the gravitational acceleration and the pipe inclination angle; the linear partial differential equations are converted into a unified linear partial differential equation as follows: Among them, u is the gas network state quantity, which is gas pressure p and flow q respectively, T is the transpose sign; K1 and K2 are constant coefficient matrices, as shown in the following formula: S2.

2. Use the central difference quotient and implicit difference scheme to convert the unified linear partial differential equation into an algebraic equation for approximate solution, as shown below: Among them, i and t are the spatial grid number and the time grid number respectively, μ 1-3 is a constant coefficient matrix, Δt g is the gas grid state estimation execution cycle, i.e., the differential time step; Δx g is the difference space step size, E is the second-order unit matrix, S2.

3. Based on the algebraic equation in step S2.2, construct the relationship between the state quantities of adjacent time-section branches: in, and are the branch state quantities at time t-1 and time t, respectively, where is relative to Initial conditions; is the boundary condition at time t, including the state quantity of the branch head end at time t-1 and time t; M is the number of branch space difference segments; χ and ε are constant coefficient matrices with dimensions of M×M and M×2, respectively, expressed as: in, S2.4, the boundary conditions in Merge to initial conditions In the process, construct the terminal state of the branch at time t The function expression is: Where, is the state quantity of the branch terminal at time t; α and β are the transfer matrices of the adjusted boundary conditions and initial conditions, respectively; S2.

5. For each branch in the natural gas network, the state quantity u is represented by gas pressure p and flow q, and the time domain model of the gas network branch is obtained by reclassification and sorting, as shown in the following formula: in, is the N-dimensional column vector of the gas pressure and gas composition at the beginning and end of the branch; α1, α2, α3 and α4 are the N×N-dimensional transfer matrices of the state quantity at the beginning to the state quantity at the end; N-dimensional column vector of initial conditions to terminal state quantities.

4. The distributed robust estimation method for the electric-gas integrated energy system based on the time domain model according to claim 1 is characterized in that: Step S3 includes the following sub-steps: S3.

1. Based on the conservation of node injection flow and the fact that the pressure at the beginning and end of a branch is equal to the pressure at the node, a natural gas network topology constraint is added to the branch time domain model, as follows: in, Inject traffic into the node; is the pressure at each node; A in and A out A is the node-branch inflow and outflow association matrix; pn1 and A pn2 is the branch-end node association matrix; S3.2, using the matrix block method to transform the branch time domain model into a node pressure p 0 / M Characterize the flow rate at the beginning and end of the branch q 0 / M The function expression is as follows: Among them, K 11 , K 12 , K 21 , K 22 is an N×N dimensional constant coefficient matrix; is an N-dimensional column vector; S3.

3. Combine the network topology of step S3.1 and the function expression of step S3.2 to construct the network time domain model as follows: Among them, Y n is the generalized admittance matrix of the natural gas network; b t is the equivalent component determined by the system state at the previous moment, Y n and b t The analytical expression is as follows: Y n =(A in K 21 -A out K 11 )A pn1 +(A in K 22 -A out K 12 )A pn2 , 5. The distributed robust estimation method for the electric-gas integrated energy system based on the time domain model according to claim 4 is characterized in that: Step S4 includes the following sub-steps: S4.

1. In the time domain model of the gas network branch The functional relationship with the node pressure at the previous moment is expressed as follows: Among them, β1, β2, β3, and β4 are the state quantities of the head end. The N×N dimensional transfer matrix; For the remaining state pairs N-dimensional transfer column vector; S4.2, for step S3.3 b t The analytical expression of is rewritten as follows: Among them, K 31 , K 32 and Y b is an N×N dimensional constant coefficient matrix, Transfer component for the state of the previous moment; S4.3, according to the network time domain model, b t Substituting the analytical expression of into the network time domain model, we get the following expression: The gas network state equation is further obtained as follows: Among them, F g and is the state transfer matrix and control variables of the gas network; during the calculation process, F g is a constant coefficient matrix; The flow injected by each node at the current moment Its state transfer component at the previous moment Related, F g and Obtained through offline calculation, The prediction is obtained by Holt's two-parameter exponential smoothing method; S4.

4. Measure the node pressure p according to the gas network volume n , node injection traffic q n and the branch head and end flow q 0 / M , the measurement equation for constructing the gas network is as follows: S4.

5. Construct the state space model of the gas network based on the state equation and measurement equation, as follows: in, is the gas network state quantity, For gas network quantity measurement; H g and It is the gas network measurement coefficient matrix and system state transfer component; is the process noise vector and is the measurement noise vector and 6. The distributed robust estimation method for the electric-gas integrated energy system based on the time domain model according to claim 5 is characterized in that: Step S5 includes the following sub-steps: S5.

1. According to the grid state quantity: node voltage amplitude V i and voltage phase angle θ i , and establish the state equation of the power grid based on Holt's two-parameter exponential smoothing method; according to the power grid quantity measurement: node voltage V i , node injection power P i , Q i And the branch power P ij , Q ij , construct the state space model corresponding to the power grid, as follows: in, and are the state and quantity measurements of the power grid at time t; Obtained by Holt's quadratic exponential smoothing method; is the power grid measurement equation; is the process noise vector and is the measurement noise vector and S5.

2. Based on the energy conversion relationship between the gas turbine and the electric hydrogen generator, the coupling element model is constructed as follows: Among them, P GT and P P2G The electric power output / consumed by the gas turbine and the electric hydrogen production unit; q GT and q P2G The gas flow rate burned / generated by the gas turbine and the electric hydrogen production unit; η GT and η P2G is the energy conversion coefficient of the gas turbine and the electric hydrogen production unit.

7. The distributed robust estimation method for the electric-gas integrated energy system based on the time domain model according to claim 6 is characterized in that: Constructing a distributed robust state estimation model for the electricity-gas integrated energy system in step S6 includes the following sub-steps: S6.1.

1. Calculate the predicted state values of the power grid and gas grid, and the predicted covariance matrix of the power grid and gas grid according to the following formula: in, are the estimated state values of the power grid and gas grid at time t-1, and the estimated covariance of the power grid and gas grid respectively; and are the state prediction values of the power grid and gas grid at time t, and the prediction covariance of the power grid and gas grid respectively; S6.1.

2. Calculate the estimated values and estimated covariance matrix of the power grid and gas grid states according to the following formula: in, are the estimated values and covariances of the power grid and gas grid states before interaction of boundary information, respectively; is the state estimated covariance The inverse matrix of is the intermediate vector, where S6.1.

3. Boundary information exchange is performed according to the following formula: in, η cp is the energy conversion coefficient set; for The part corresponding to the injection flow of the coupling node of the gas network; The predicted value of active power injected into the grid coupling node; when When , where υ is the convergence threshold, the boundary information interaction ends; Inject active power estimation values into the nodes associated with gas turbines and hydrogen production units in the electric-gas integrated energy system. and Inject the active power estimation covariance for the nodes associated with the gas turbine and the hydrogen generator: S6.1.4, the process noise adaptive correction algorithm is as follows: Among them, d t is the weight coefficient; is the difference between the estimated value and the predicted value at time t; is the Kalman gain matrix; is the measurement prediction covariance matrix, which can be expressed as: Where b is the forgetting factor and 0.95≤b≤0.995; S6.1.5, the measurement noise adaptive correction algorithm is as follows: in, is the corrected measurement noise variance matrix; is the correction scale matrix; c is the threshold; is the i-th normalized residual component of the measurement prediction value; and is the i-th component of the measurement prediction value and prediction variance matrix.

8. The distributed robust estimation method for the electric-gas integrated energy system based on the time domain model according to claim 7 is characterized in that: The step S6 of constructing the grid state estimation model includes the following sub-steps: S6.2.

1. Calculate the grid state prediction value and prediction covariance matrix according to the following formula: in, are the estimated state value and estimated covariance of the power grid at time t-1 respectively; and are the state prediction value and prediction covariance of the power grid at time t respectively; S6.2.

2. Calculate the grid state estimate and estimated covariance matrix according to the following formula: in, are the estimated value and covariance of the power grid state with no boundary information interaction; is the state estimated covariance The inverse matrix of is the intermediate vector, where S6.2.3, the process noise adaptive correction algorithm is as follows: Among them, d t is the weight coefficient; is the difference between the estimated value and the predicted value of the power grid state at time t; is the Kalman gain matrix; is the measurement prediction covariance matrix, which can be expressed as: Where b is the forgetting factor and 0.95≤b≤0.995; S6.2.4, the measurement noise adaptive correction algorithm is as follows: in, is the corrected measurement noise variance matrix; is the correction scale matrix; c is the threshold; is the i-th normalized residual component of the measurement prediction value; and is the i-th component of the measurement prediction value and prediction variance matrix.

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